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electric potential

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• Khan Academy - Electric potential
• BCCampus Publishing - Electric Potential in a Uniform Electric Field
• Physics LibreTexts - Electric Potential
• Pressbooks Create - Introduction to Physics - Electric Potential Energy and Electric Potential
• Massachusetts Institute of Technology - Electric Potential
• The University of Texas at Austin - Department of PPhysics - Electric Potential and Electric Field
• National Center for Biotechnology Information - Electric Potential and Capacitance
• University of Saskatchewan Pressbooks - Electric Potential and Potential Difference
• Physics classroom - Electric potential

electric potential , the amount of work needed to move a unit charge from a reference point to a specific point against an electric field . Typically, the reference point is Earth , although any point beyond the influence of the electric field charge can be used.

The diagram shows the forces acting on a positive charge q located between two plates, A and B, of an electric field E . The electric force F exerted by the field on the positive charge is F = qE; to move the charge from plate A to plate B, an equal and opposite force ( F ′ = − qE ) must then be applied. The work W done in moving the positive charge through a distance d is W = F ′ d = − qEd.

The potential energy for a positive charge increases when it moves against an electric field and decreases when it moves with the electric field; the opposite is true for a negative charge. Unless the unit charge crosses a changing magnetic field , its potential at any given point does not depend on the path taken.

Although the concept of electric potential is useful in understanding electrical phenomena, only differences in potential energy are measurable. If an electric field is defined as the force per unit charge, then by analogy an electric potential can be thought of as the potential energy per unit charge. Therefore, the work done in moving a unit charge from one point to another (e.g., within an electric circuit ) is equal to the difference in potential energies at each point. In the International System of Units (SI), electric potential is expressed in units of joules per coulomb (i.e., volts ), and differences in potential energy are measured with a voltmeter .

23 Electric Potential

Introduction to potential, instructor’s note.

By the end of this section you should know that the electric force is conservative (i.e. there is a potential energy associated with the electric force), you should be able to define what a potential is and be able to calculate potential energy from a potential.

We will begin by stating that the electric force is a conservative force, which means that an electric potential energy must exist. In one of your problems, you will explore the idea of work done by a charge moving in a uniform electric field. You will see that as the charge moves around the work done is independent of the path of the charged takes, and that the work done around a closed loop path is in fact zero. This fact that the work done around a closed loop path is indicative of the fact that the electric field must be a conservative force, this should be familiar to you from previous sections.

We’ve actually been using the idea of electric potential energy already, throughout both this class and Physics 131. The chemical energies discussed in Physics 131 are actually electric potential energies. Similarly, the potential energies of the electrons that we discussed in Units 1 and 2, unless we stated explicitly that they were gravitational potential energies, were electric potential energies.

What is the electric potential? In the figure below, we have an electron surrounding a nucleus.

The question arises from the same place as our discussion of electrical forces, how does the electron know that the nucleus is there?

There’s a deep connection between electric field and electric potential that will be explored in a later section. Just as with electric field the potential exists even if there is something to feel there or not, so even if we were to remove the electron the potential would still be present.

is why some people call potential, potential energy per unit charge. On the other hand, I want you to think of it as an invisible field around charges, that gives rise to potential energy when other charged particles interact with it.

Now, let’s do an example

What are the initial and final potential energies? What is the change in potential energy?

Let’s begin by looking at the initial potential energy

Even though the potential dropped from 10V to 5V, the potential energy actually increased . This is due to the fact that the electron has a negative charge.

Once we have changes in potential energy, we can then move on to solve problems using conservation of energy as we’ve been doing throughout this course.

One last point to discuss is the connection between the volt and the electron volt. You may have already started to see this connection in the last problem. Throughout this course and in Physics 131 we’ve been using the electron volt as a unit of energy, and we’ve just been using it as a straight conversion factor,

Now however, you have enough information to understand where this unit of energy comes from: 1eV is the increase in energy of an electron as it goes across a 1-volt potential drop. To solve it out, we know

In Summary:

• Potential is to potential energy as electric field is to electric force
• Forces result in charged objects interacting, forces result from charged particles interacting with the fields generated by other charged objects through
• Potential energies result from charged objects interacting with the potentials generated by other charged objects, mathematically written as
• Fields and potentials have the same sort of relationship as forces and potential energies
• We can solve many problems by looking at it either in terms of fields and potentials, just like we can solve many problems by looking at it in terms of forces or potential energies
• The unit of the potential is the volt, where one volt is equal to one Joule per Coulomb and the electron volt as a unit of energy arises from the amount of energy gained by an electron going across a one-volt potential difference.

Some Common Misconceptions About Potential

The familiar term  voltage  is the common name for potential difference. Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between two points. For example, every battery has two terminals, and its voltage is the potential difference between them. More fundamentally, the point you choose to be zero volts is arbitrary. This is analogous to the fact that gravitational potential energy has an arbitrary zero, such as sea level or perhaps a lecture hall floor.

In summary, the relationship between potential difference (or voltage) and electrical potential energy is given by

Calculating Energy

Suppose you have a 12.0 V motorcycle battery that can move 5000 C of charge, and a 12.0 V car battery that can move 60,000 C of charge. How much energy does each deliver? (Assume that the numerical value of each charge is accurate to three significant figures.)

So to find the energy output, we multiply the charge moved by the potential difference.

While voltage and energy are related, they are not the same thing. The voltages of the batteries are identical, but the energy supplied by each is quite different. Note also that as a battery is discharged, some of its energy is used internally and its terminal voltage drops, such as when headlights dim because of a low car battery. The energy supplied by the battery is still calculated as in this example, but not all of the energy is available for external use.

How Many Electrons Move through a Headlight Each Second?

When a 12.0 V car battery runs a single 30.0 W headlight, how many electrons pass through it each second?

This is a very large number. It is no wonder that we do not ordinarily observe individual electrons with so many being present in ordinary systems. In fact, electricity had been in use for many decades before it was determined that the moving charges in many circumstances were negative. Positive charge moving in the opposite direction of negative charge often produces identical effects; this makes it difficult to determine which is moving or whether both are moving.

Problem 14: A lightning bolt strikes a tree, moving charge through a potential difference. What energy was dissipated?

Problem 15: An evacuated tube uses an accelerating voltage to accelerate electrons to hit a copper plate and produce x rays. What would be the final speed of such an electron?

Electrical Potential Due to a Point Charge

What Voltage Is Produced by a Small Charge on a Metal Sphere?

Entering known values into the expression for the potential of a point charge, we obtain

The negative value for voltage means a positive charge would be attracted from a larger distance, since the potential is lower (more negative) than at larger distances. Conversely, a negative charge would be repelled, as expected.

What Is the Excess Charge on a Van de Graaff Generator

A demonstration Van de Graaff generator has a 25.0 cm diameter metal sphere that produces a voltage of 100 kV near its surface. (See Figure 1.) What excess charge resides on the sphere? (Assume that each numerical value here is shown with three significant figures.)

The potential on the surface will be the same as that of a point charge at the center of the sphere, 12.5 cm away. (The radius of the sphere is 12.5 cm.) We can thus determine the excess charge using the equation

This is a relatively small charge, but it produces a rather large voltage. We have another indication here that it is difficult to store isolated charges.

Homework Problems

Problem 16: What is the potential 52.92 pm from a proton (the average distance between the proton and electron in a hydrogen atom)?

Problem 17: A research Van de Graaff generator has a metal sphere with a charge on it. What is the potential near its surface?

Equipotential Lines

One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. This implies that a  conductor is an equipotential surface in static situations .  There can be no voltage difference across the surface of a conductor, or charges will flow.

Because a conductor is an equipotential, it can replace any equipotential surface. For example, in Figure 1 a charged spherical conductor can replace the point charge, and the electric field and potential surfaces outside of it will be unchanged, confirming the contention that a spherical charge distribution is equivalent to a point charge at its center.

Figure 2 shows the electric field and equipotential lines for two equal and opposite charges. Given the electric field lines, the equipotential lines can be drawn simply by making them perpendicular to the electric field lines. Conversely, given the equipotential lines, as in Figure 3(a), the electric field lines can be drawn by making them perpendicular to the equipotentials, as in Figure 3(b).

Section Summary

• An equipotential line is a line along which the electric potential is constant.
• An equipotential surface is a three-dimensional version of equipotential lines.
• Equipotential lines are always perpendicular to electric field lines.

Problem 18: Electric field lines are always___________.

Problem 19: Electric field lines ____________.

The Relationship Between Electric Potential and Electric Field

In Figure 6 we see the two approaches applied to a nucleus attracting an electron. In one picture, the nucleus generates an electric field

The magnitude of the electric field is the change in potential between the two points divided by the distance between those two points. This is a slope (i.e. derivative) thing like velocity or acceleration: to get the electric field at a point, you need to look at the change in potential immediately on either side and divide by the tiny distance between them. Only for uniform fields will this equation give exact results, otherwise it gives an average electric field value.

(The fact that we end up with an obviously true statement of N/C = N/C means that our starting assertion that N/C = V/m was true). Since Volts are much easier to measure and control in the lab, the units of V/m are probably more commonly used than N/C.

There is one final issue we need to address: the electric field is a vector having magnitude and direction, while the potential is a scalar , having only a magnitude. How can we determine the direction? Again, we turn to gravity for an analogy. We notice that the force of gravity points towards lower potential energy (down the hill). This is true for electricity as well: the electric field points down the “potential hill.” In the example in Figure 6 above, the electric potential from the nucleus decreases with distance and the electric field points away from the nucleus. In general, the electric field points down the steepest slope in electric potential. We write this mathematically as

where the negative sign tells us that the electric field points down hill: from one equipotential to the next lower, always perpendicular to the equipotential lines as described in the previous section. We will practice this idea more in class.

What is the Highest Voltage Possible between Two Plates?

The potential difference or voltage between the plates is

(The answer is quoted to only two digits, since the maximum field strength is approximate.)

One of the implications of this result is that it takes about 75 kV to make a spark jump across a 2.5 cm (1 in.) gap, or 150 kV for a 5 cm spark. This limits the voltages that can exist between conductors, perhaps on a power transmission line. A smaller voltage will cause a spark if there are points on the surface, since points create greater fields than smooth surfaces. Humid air breaks down at a lower field strength, meaning that a smaller voltage will make a spark jump through humid air. The largest voltages can be built up, say with static electricity, on dry days.

Field and Force inside an Electron Gun

Solution for (a)

The expression for the magnitude of the electric field between two uniform metal plates is

Solution for (b)

The magnitude of the force on a charge in an electric field is obtained from the equation

Substituting known values gives

Problem 20: Which of the following are units of electric field?

Problem 21: Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. What is the voltage across a membrane given an electric field strength across it?

Problem 22: What is the potential difference between the plates given the electric field and separation? The plate with the lowest potential is taken to be at zero volts. What is the potential 1.0 "> 1.0 cm "> cm from that plate?

Problem 23: Find the maximum potential difference between two parallel conducting plates separated by some amount of air, given the maximum sustainable electric field strength in air to be 3.00 MV/m.

A PhET to Explore These Ideas

A few things to play around with in the simulation above:

1. Add a positive and negative charge with about 5 cm of space between them. Describe what the electric field looks like.

2. Use the device to plot equipotential lines (locations where the electric potential is the same). Describe what the equipotentials look like.

3. Is there a relationship between the electric field and the equipotentials?

4. What happens if you add more charges?

Physics 132: What is an Electron? What is Light? by Roger Hinrichs, Paul Peter Urone, Paul Flowers, Edward J. Neth, William R. Robinson, Klaus Theopold, Richard Langley, Julianne Zedalis, John Eggebrecht, and E.F. Redish is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Electric Potential

Claimed by Neal Austensen Fall2023

• 1.1 A Mathematical Model
• 1.2 A Computational Model
• 2.2 Middling
• 2.3 Difficult
• 3 Connectedness
• 5.1 Further reading
• 5.2 Externals links
• 6 References
• 7 The Main Idea
• 8.1 Middling
• 8.2 Difficult
• 9 Connectedness
• 11.1 External Links
• 12 References

The Main Idea

Electric Potential Energy , like all forms of potential energy, is the potential for work to be done, in this case by the electric force. The Electric Potential (frequently referred to as voltage, from its SI unit, the Volt) is the Electric Potential Energy associated with the test charge (1 Coulomb), such that it depends only on the source, just as the electric field is related to the electric force, but depends only on the source. One may similarly remember the parallel concept of the gravitational potential, which was gravitational potential energy divided by mass.

A Mathematical Model

Electric Potential Energy is defined with respect to the Electric Force & Electric Field :

The differential work [math]\displaystyle{ (dW) }[/math] associated with an external force [math]\displaystyle{ (\mathbf{F}_{ext}) }[/math] moving a charge [math]\displaystyle{ (q) }[/math] from point b to point a [math]\displaystyle{ (d\mathbf{L}) }[/math] through an electric field [math]\displaystyle{ (\mathbf{E}) }[/math] is:

The external force must be equal and opposite to the force associated with the source charge's electric field:

Integrating from point b to point a along the path gives:

Finally, since the work was defined externally, the calculated work is equal to the Electric Potential Energy :

From this, the Electric Potential is defined as the Electric Potential Energy per test charge in the source charge's electric field:

• The electric field is a conservative vector field :
• A special case shown in dark green near the bottom right of the figure also exists:

• The Electric Potential from a source charge [math]\displaystyle{ (Q) }[/math] can be written in a simpler expression:
• The initial position is often taken to be infinity (the Electric Potential is defined to be zero at infinity) creating a simpler and more familiar looking equation:

If a charge [math]\displaystyle{ (q) }[/math] is being moved in a source charge's [math]\displaystyle{ (Q) }[/math] electric field [math]\displaystyle{ (\mathbf{E}) }[/math] the Electric Potential Energy is:

The electric field is known to be described radially as: ( Electric Field )

Allow the path be along the radial direction:

Plugging these in gives:

Therefore, the Electric Potential is:

• Critical Formulas

A Computational Model

Click on the link to see Electric Potential through VPython! Make sure to press "Run" to see the principle in action!

Click the link below and press run to see a visual model of electric potential in space with equal and opposite charges (Press "Run")

Watch this video for a more visual approach!

A parallel plate capacitor is shown below:

Each plate has area [math]\displaystyle{ A }[/math] with positive charge [math]\displaystyle{ Q }[/math] on the left plate and negative charge [math]\displaystyle{ -Q }[/math] on the right plate. The distance between the plates is [math]\displaystyle{ d }[/math] .

• Question 1 :

Electric fields always point from positive to negative charge. Therefore, the electric field between the plates will point in the positive [math]\displaystyle{ x }[/math] -direction, straight from the left plate to the right plate since the distribution of positive and negative charge is flat and symmetric. The electric field will bend near the edges (called fringing fields). These are usually neglected if [math]\displaystyle{ d }[/math] is much smaller than the length of the plates.

• Question 2 :

We start with noting that the charge ( [math]\displaystyle{ q_n=-\alpha q, \alpha \gt 0 }[/math] ) in question is a negative charge. This effectively means all analysis will be reversed i.e. if the electric potential energy was increasing for a positive charge, it would be decreasing for a negative charge. With that said, we can start by noticing that the charge is moving against the electric field between the plates. Since this a negative charge, this is the way that negative charge wants to move, meaning it is losing electric potential energy and gaining kinetic energy. This can be seen mathematically by the following:

[math]\displaystyle{ U_{ab} = -q \int_b^a \mathbf{E} \cdot d \mathbf{L} = - (q_n) (-E_o) \Delta L = (-\alpha q)E_o \Delta L = -\alpha q E_o \Delta L }[/math] (since the electric field is approximately constant between the plates & the electric field and path are aligned)

We can readily see that moving from position [math]\displaystyle{ b }[/math] to position [math]\displaystyle{ a }[/math] (a distance of length [math]\displaystyle{ \Delta L }[/math] ) causes a decrease in electric potential energy since this is a negative charge.

Now dividing [math]\displaystyle{ U_{ab} }[/math] by [math]\displaystyle{ q_n }[/math] gives [math]\displaystyle{ V_{ab} }[/math] :

[math]\displaystyle{ V_{ab} = \frac{U_{ab}}{q_n} = \frac{U_{ab}}{-\alpha q} = E_o \Delta L }[/math]

Therefore the electric potential is increasing.

• Question 3 :

We can reverse our answer from b. but keep in mind electric potential is per unit test charge ...essentially it is charge independent. Therefore, the electric potential energy of the positive charge would be increasing ( [math]\displaystyle{ \alpha q E_o \Delta L }[/math] ), and the electric potential would still be increasing.

A positive charge [math]\displaystyle{ q_o }[/math] travels through a spatially uniform electric field from Point [math]\displaystyle{ A }[/math] to Point [math]\displaystyle{ B }[/math] to Point [math]\displaystyle{ C }[/math] , was depicted in the figure below. The coordinates of the points and magnitude of the electric field are defined in the figure.

[math]\displaystyle{ V_{AB} = - \int_B^A \mathbf{E} \cdot d \mathbf{L} }[/math]

In this case, the electric field is a constant [math]\displaystyle{ (E_o, 0) }[/math] , and the path is a straight line with components: [math]\displaystyle{ \Delta \mathbf{L} = A-B = (0, 0) - (6, -3) = (-6, 3) }[/math]

Our expression for the change in electric potential simplifies to: [math]\displaystyle{ V_{AB} = -\mathbf{E} \cdot \Delta \mathbf{L} = -(E_o, 0) \cdot (-6, +3) = 6E_o = 6E_o = 300 \ \mathrm{V} }[/math]

The process is exactly the same as part a: [math]\displaystyle{ V_{BC} = -\int_C^B \mathbf{E} \cdot \Delta \mathbf{L} = - (E_o, 0) \cdot (1, -4) = -E_o = -50 \ \mathrm{V} }[/math]

We repeat the same process again: [math]\displaystyle{ V_{AC} = -\int_C^A \mathbf{E} \cdot \Delta \mathbf{L} = - (E_o, 0) \cdot (-5, 1) = 5E_o = 250 \ \mathrm{V} }[/math]

The three calculated electric potential differences are related by: [math]\displaystyle{ V_{AC} = V_{AB} + V_{BC} = 250 \ \mathrm{V} }[/math]

This illustrates the path independence of the potential difference, and thus the conservative nature of the electric field.

Connectedness

The concept of electric potential has a long, illustrious history that dates back many centuries. Otto von Guericke, William Gilbert, and Robert Boyle were among the pioneering scientists who contributed to the study of electricity in the 17th century. The idea of electric potential did not start to take form until the 18th century, however.

French scientist Charles Du Fay discovered in 1733 that friction could charge certain materials, including amber, and that this charge could be transmitted to other things. Du Fay also observed that depending on the sign of their charges, two charged items might either attract or repel one another when placed near to one another.

Both Dutch scientist Pieter van Musschenbroek and German physicist Ewald Georg von Kleist independently devised the Leyden jar, a device that could hold an electric charge, in 1745. The Leyden jar was simply a glass jar with a wire or rod put through the cork and either water or metal foil within. The charge would be kept in the jar until the wire was charged.

Charles-Augustin de Coulomb, a French scientist, first proposed the idea of electric potential energy in 1785. In an electric field, Coulomb demonstrated that the amount of labor needed to transfer a charged particle from one location to another was proportional to the difference in electric potential between the two sites. In the 19th century, Scottish scientist James Clerk Maxwell and German physicist Georg Simon Ohm expanded on this idea.

Electric potential is a key idea in physics today and is applied in a variety of domains, including electronics, electrical engineering, and the study of charged particle behavior in electromagnetic fields.

Further reading

Externals links.

Calculate the change in electric potential between point A, which is at [math]\displaystyle{ (-4, 3,0) \; m }[/math] , and B, which is at [math]\displaystyle{ (2,-2,0) \; m }[/math] . The electric field in the location is [math]\displaystyle{ (50,0,0) \; N/C }[/math] .

Answer: -300V

Explanation:

[math]\displaystyle{ \Delta\vec{l}= (2,-2,0)\;m - (-4,3,0)\;m = (6,-5,0)\;m }[/math]

[math]\displaystyle{ \Delta{V} = -({E}_{x}∆{x} + {E}_{y}∆{y} + {E}_{z}∆{z}) }[/math]

[math]\displaystyle{ \Delta{V} = -(50\; N/C \cdot 6 \;m + 0 \; N/c \cdot -5 \; m + 0\cdot 0) }[/math]

[math]\displaystyle{ \Delta{V} = -300 V }[/math]

The Bohr Model of the hydrogen atom treats it as a nucleus of charge [math]\displaystyle{ +e }[/math] electrons of charge [math]\displaystyle{ -e }[/math] orbiting in circular orbits of specific radii. Calculate the potential difference between two points, one infinitely far away from the nucleus, and the other one Bohr radius [math]\displaystyle{ a_0 }[/math] away from the nucleus (don't worry about substituting in the values). Compute the electric potential energy associated with the electron one Bohr radius away from the nucleus, setting the potential energy at infinity as zero (remember the sign of the charge).

We may compute the electric potential by taking integrating the electric field of a point charge as the radius goes from infinity to [math]\displaystyle{ a_0 }[/math] . This integral may be set up as:

[math]\displaystyle{ \Delta V = -\int_\infty^{a_0} \vec{E}\cdot\text{d}\vec{l} }[/math]

[math]\displaystyle{ \Delta V = -\frac{e}{4\pi\epsilon_0} \int_\infty^{a_0} \frac{\text{d} r}{r^2} }[/math]

This may then be solved:

[math]\displaystyle{ \Delta V = \frac{e}{4\pi\epsilon_0}\biggr{(}\frac{1}{r}\biggr{|}_\infty^{a_0} = \frac{e}{4\pi\epsilon_0 a_0} }[/math]

to compute the potential energy, we now multiply by the charge of the electron: [math]\displaystyle{ -e }[/math] , giving

[math]\displaystyle{ U = -\frac{e^2}{4\pi\epsilon_0 a_0} }[/math]

Depending on what physics or chemistry courses you may have taken before, this may be recognizable as twice the ionization energy of the n=1 orbital. The factor of two is due to the fact that in the Bohr model, the kinetic energy will be exactly half of this potential energy, and will be positive so that the net result is still negative, but with half the magnitude. This understanding of the hydrogen atom gets certain values right, but the reality of the situation is far more complicated.

How is this topic connected to something that you are interested in?

[Author] I am interested in robotic systems and building circuit boards and electrical systems for manufacturing robots. While studying this section in the book, I was able to connect back many of the concepts and calculations back to robotics and the electrical component of automated systems.

[Revisionist] Since high school, I never really understood how to work with the voltmeter and what it measured, and I have always wanted to know, but although this particular wiki page did not go into the details and other branches of electric potential, it led me to find the answers to something I was interested in since high school, the concept of electric potential.

[Editor] I think electively is really interesting. When I was younger, I participated in this demo where a group of people hold hands and someone touches this special ball full of charge. We all could feel the tingling sensation of the current passing through us. It’s cool to learn the theory behind the supposed magic that occurs.

[FALL 2018] I think it's very interesting that electric potential can be seen as a property of a space and that we can have further applications using this property.

How is it connected to your major?

[Author] I am a Mechanical Engineering major, so I will be dealing with the electrical components of machines when I work. Therefore, I have to know these certain concepts such as electric potential in order to fully understand how they work and interact.

[Revistionist] As a biochemistry major, electric potential and electric potential difference is not particularly related to my major, but in chemistry classes, we use electrostatic potential maps (electrostatic potential energy maps) that shows the charge distributions throughout a molecule. Although the main use in electric potential is different in physics and biochemistry (where physicists use it identify the effect of the electric field at a location), I still found it interesting as the concept of electric potential (buildup) was being used in quite a different way.

[Editor] I am a computer science major. Although I deal mostly with software, the hardware aspect is still important. The algorithms that I design run differently on different machines. The time complexity of an algorithm is sometimes useless when worrying about constant factors that are determined by a system’s hardware. Quicksort, for instance, is usually faster than many other sorts that have lower time complexities. The hardware of computers heavily relies on electricity and current (which is induced by a potential difference) to switch transistors on and off and thereby process information.

[FALL 2018] I am an aerospace engineering major, and I think understanding such concepts will help me have a better holistic understanding towards fields and systems. In addition, the thinking behind solving related problems will help me better prepared for future classes that involve with solving dynamics problems.

Is there an interesting industrial application?

[Author] Electrical potential is used to find the voltage across a path. This is useful when working with circuit components and attempting to manipulate the power output or current throughout a component.

[Revisionist] Electric potential sensors are being used to detect a variety of electrical signals made by the human body, thus contributing to the field of electrophysiology.

[Editor] The study of electric potential has lead scientists to generate very safe wires that will not overheat and cause fires. Connecting circuits to ground is important and the third prong in an electrical outlet is this ground connection.

The idea of electric potential, in a way, started with Ben Franklin and his experiments in the 1740s. He began to understand the flow of electricity, which eventually paved the path towards explaining electric potential and potential difference. Scientists finally began to understand how electric fields were actually affecting the charges and the surrounding environment. Benjamin Franklin first shocked himself in 1746, while conducting experiments on electricity with found objects from around his house. Six years later, or 261 years ago for us, the founding father flew a kite attached to a key and a silk ribbon in a thunderstorm and effectively trapped lightning in a jar. The experiment is now seen as a watershed moment in mankind's venture to channel a force of nature that was viewed quite abstractly.

By the time Franklin started experimenting with electricity, he'd already found fame and fortune as the author of Poor Richard's Almanack. Electricity wasn't a very well understood phenomenon at that point, so Franklin's research proved to be fairly foundational. The early experiments, experts believe, were inspired by other scientists' work and the shortcomings therein.

source: http://www.benjamin-franklin-history.org/kite-experiment/

That early brush with the dangers of electricity left an impression on Franklin. He described the sensation as "a universal blow throughout my whole body from head to foot, which seemed within as well as without; after which the first thing I took notice of was a violent quick shaking of my body." However, it didn't scare him away. In the handful of years before his famous kite experiment, Franklin contributed everything from designing the first battery designs to establishing some common nomenclature in the study of electricity. Although Franklin is often coined the father of electricity, after he set the foundations of electricity, many other scientists contributed his or her research in the advancement of electricity and eventually led to the discovery of electric potential and potential difference.

Like mentioned multiple times throughout the page, although electric potential is a huge and important topic, it has many branches, which makes the concept of electric potential difficult to stand alone. Even with this page, to support the concept of electric potential, many crucial branches of the topic appeared, like potential difference (which also branched into [ Potential Difference Path Independence ], [ Potential Difference In A Uniform Field ], and [ Potential Difference In A Nonuniform Field ]).

External Links

[1] https://www.khanacademy.org/test-prep/mcat/physical-processes/electrostatics-1/v/electric-potential-at-a-point-in-space

[2] https://www.youtube.com/watch?v=pcWz4tP_zUw

[3] https://www.youtube.com/watch?v=Vpa_uApmNoo

[4] https://www.khanacademy.org/science/electrical-engineering/ee-electrostatics/ee-fields-potential-voltage/a/ee-electric-potential-voltage

[1] "Benjamin Franklin and Electricity." Benjamin Franklin and Electricity. N.p., n.d. Web. 17 Apr. 2016. < http://www.americaslibrary.gov/aa/franklinb/aa_franklinb_electric_1.html >.

[2] Bottyan, Thomas. "Electrostatic Potential Maps." Chemwiki. N.p., 02 Oct. 2013. Web. 17 Apr. 2016. < http://chemwiki.ucdavis.edu/Core/Theoretical_Chemistry/Chemical_Bonding/General_Principles_of_Chemical_Bonding/Electrostatic_Potential_maps >.

[3] "Electric Potential Difference." Electric Potential Difference. The Physics Classroom, n.d. Web. 14 Apr. 2016. < http://www.physicsclassroom.com/class/circuits/Lesson-1/Electric-Potential-Difference >.

[4] Harland, C. J., T. D. Clark, and R. J. Prance. "Applications of Electric Potential (Displacement Current) Sensors in Human Body Electrophysiology." International Society for Industrial Process Tomography, n.d. Web. 16 Apr. 2016. < http://www.isipt.org/world-congress/3/269.html >.

[5] Sherwood, Bruce A. "2.1 The Momentum Principle." Matter & Interactions. By Ruth W. Chabay. 4th ed. Vol. 1. N.p.: John Wiley & Sons, 2015. 45-50. Print. Modern Mechanics.

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7.3 Calculations of Electric Potential

Learning objectives.

By the end of this section, you will be able to:

• Calculate the potential due to a point charge
• Calculate the potential of a system of multiple point charges
• Describe an electric dipole
• Define dipole moment
• Calculate the potential of a continuous charge distribution

Point charges, such as electrons, are among the fundamental building blocks of matter. Furthermore, spherical charge distributions (such as charge on a metal sphere) create external electric fields exactly like a point charge. The electric potential due to a point charge is, thus, a case we need to consider.

We can use calculus to find the work needed to move a test charge q from a large distance away to a distance of r from a point charge q . Noting the connection between work and potential W = − q Δ V , W = − q Δ V , as in the last section, we can obtain the following result.

Electric Potential V of a Point Charge

The electric potential V of a point charge is given by

where k is a constant equal to 8.99 × 10 9 N · m 2 /C 2 . 8.99 × 10 9 N · m 2 /C 2 .

The potential at infinity is chosen to be zero. Thus, V for a point charge decreases with distance, whereas E → E → for a point charge decreases with distance squared:

Recall that the electric potential difference V is a scalar and has no direction, whereas the electric field E → E → is a vector. To find the voltage due to a combination of point charges, given zero voltage at infinitely far away, you add the individual voltages as numbers. We will assume for the rest of this chapter that there is zero voltage measured infinitely far away. To find the total electric field, you must add the individual fields as vectors, taking magnitude and direction into account. This is consistent with the fact that V is closely associated with energy, a scalar, whereas E → E → is closely associated with force, a vector.

Example 7.10

What voltage is produced by a small charge on a metal sphere, significance, example 7.11, what is the excess charge on a van de graaff generator, check your understanding 7.8.

What is the potential inside the metal sphere in Example 7.10 ?

The voltages in both of these examples could be measured with a meter that compares the measured potential with ground potential. Ground potential is often taken to be zero (instead of taking the potential at infinity to be zero). It is the potential difference between two points that is of importance, and very often there is a tacit assumption that some reference point, such as Earth or a very distant point, is at zero potential. As noted earlier, this is analogous to taking sea level as h = 0 h = 0 when considering gravitational potential energy U g = m g h U g = m g h .

Systems of Multiple Point Charges

Just as the electric field obeys a superposition principle, so does the electric potential. Consider a system consisting of N charges q 1 , q 2 , … , q N . q 1 , q 2 , … , q N . What is the net electric potential V at a space point P from these charges? Each of these charges is a source charge that produces its own electric potential at point P , independent of whatever other changes may be doing. Let V 1 , V 2 , … , V N V 1 , V 2 , … , V N be the electric potentials at P produced by the charges q 1 , q 2 , … , q N , q 1 , q 2 , … , q N , respectively. Then, the net electric potential V P V P at that point is equal to the sum of these individual electric potentials. You can easily show this by calculating the potential energy of a test charge when you bring the test charge from the reference point at infinity to point P :

Note that electric potential follows the same principle of superposition as electric field and electric potential energy. To show this more explicitly, note that a test charge q t q t at the point P in space has distances of r 1 , r 2 , … , r N r 1 , r 2 , … , r N from the N charges fixed in space above, as shown in Figure 7.19 . Using our formula for the potential of a point charge for each of these (assumed to be point) charges, we find that

Therefore, the electric potential energy of the test charge is

which is the same as the work to bring the test charge into the system, as found in the first section of the chapter.

The Electric Dipole

An electric dipole is a system of two equal but opposite charges a fixed distance apart. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is the same as heat at the molecular level.

Example 7.12

Electric potential of a dipole.

• V P = k e ∑ 1 N q i r i = ( 9.0 × 10 9 N · m 2 / C 2 ) ( 3.0 nC 0.010 m − 3.0 nC 0.030 m ) = 1.8 × 10 3 V V P = k e ∑ 1 N q i r i = ( 9.0 × 10 9 N · m 2 / C 2 ) ( 3.0 nC 0.010 m − 3.0 nC 0.030 m ) = 1.8 × 10 3 V
• V P = k e ∑ 1 N q i r i = ( 9.0 × 10 9 N · m 2 / C 2 ) ( 3.0 nC 0.070 m − 3.0 nC 0.030 m ) = −5.1 × 10 2 V V P = k e ∑ 1 N q i r i = ( 9.0 × 10 9 N · m 2 / C 2 ) ( 3.0 nC 0.070 m − 3.0 nC 0.030 m ) = −5.1 × 10 2 V
• V P = k ∑ 1 N q i r i = ( 9.0 × 10 9 N · m 2 / C 2 ) ( 3.0 nC 0.030 m − 3.0 nC 0.050 m ) = 3.6 × 10 2 V V P = k ∑ 1 N q i r i = ( 9.0 × 10 9 N · m 2 / C 2 ) ( 3.0 nC 0.030 m − 3.0 nC 0.050 m ) = 3.6 × 10 2 V

Check Your Understanding 7.9

What is the potential on the x -axis? The z -axis?

Now let us consider the special case when the distance of the point P from the dipole is much greater than the distance between the charges in the dipole, r ≫ d ; r ≫ d ; for example, when we are interested in the electric potential due to a polarized molecule such as a water molecule. This is not so far (infinity) that we can simply treat the potential as zero, but the distance is great enough that we can simplify our calculations relative to the previous example.

We start by noting that in Figure 7.21 the potential is given by

This is still the exact formula. To take advantage of the fact that r ≫ d , r ≫ d , we rewrite the radii in terms of polar coordinates, with x = r sin θ x = r sin θ and z = r cos θ z = r cos θ . This gives us

We can simplify this expression by pulling r out of the root,

and then multiplying out the parentheses

The last term in the root is small enough to be negligible (remember r ≫ d , r ≫ d , and hence ( d / r ) 2 ( d / r ) 2 is extremely small, effectively zero to the level we will probably be measuring), leaving us with

Using the binomial approximation (a standard result from the mathematics of series, when α α is small)

and substituting this into our formula for V P V P , we get

This may be written more conveniently if we define a new quantity, the electric dipole moment ,

where these vectors point from the negative to the positive charge. Note that this has magnitude qd . This quantity allows us to write the potential at point P due to a dipole at the origin as

A diagram of the application of this formula is shown in Figure 7.22 .

There are also higher-order moments, for quadrupoles, octupoles, and so on. You will see these in future classes.

Potential of Continuous Charge Distributions

We have been working with point charges a great deal, but what about continuous charge distributions? Recall from Equation 7.9 that

We may treat a continuous charge distribution as a collection of infinitesimally separated individual points. This yields the integral

for the potential at a point P . Note that r is the distance from each individual point in the charge distribution to the point P . As we saw in Electric Charges and Fields , the infinitesimal charges are given by

where λ λ is linear charge density, σ σ is the charge per unit area, and ρ ρ is the charge per unit volume.

Example 7.13

Potential of a line of charge, example 7.14, potential due to a ring of charge, example 7.15, potential due to a uniform disk of charge.

The superposition of potential of all the infinitesimal rings that make up the disk gives the net potential at point P . This is accomplished by integrating from r = 0 r = 0 to r = R r = R :

Example 7.16

Potential due to an infinite charged wire.

However, this limit does not exist because the argument of the logarithm becomes [2/0] as L → ∞ L → ∞ , so this way of finding V of an infinite wire does not work. The reason for this problem may be traced to the fact that the charges are not localized in some space but continue to infinity in the direction of the wire. Hence, our (unspoken) assumption that zero potential must be an infinite distance from the wire is no longer valid.

To avoid this difficulty in calculating limits, let us use the definition of potential by integrating over the electric field from the previous section, and the value of the electric field from this charge configuration from the previous chapter.

where R is a finite distance from the line of charge, as shown in Figure 7.26 .

With this setup, we use E → P = 2 k e λ 1 s s ^ E → P = 2 k e λ 1 s s ^ and d l → = d s → d l → = d s → to obtain

Now, if we define the reference potential V R = 0 V R = 0 at s R = 1 m, s R = 1 m, this simplifies to

Note that this form of the potential is quite usable; it is 0 at 1 m and is undefined at infinity, which is why we could not use the latter as a reference.

Check Your Understanding 7.10

What is the potential on the axis of a nonuniform ring of charge, where the charge density is λ ( θ ) = λ cos θ λ ( θ ) = λ cos θ ?

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Electric Potential, Capacitors, and Dielectrics

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This chapter continues our study of electrostatics, introducing the concepts of electric potential and capacitance. We analyze electrical circuits containing capacitors in parallel and in series, and learn how energy, electric potential, and electric charge are related in different situations. We also elucidate electrostatic phenomena inside “dielectric materials”, a.k.a. dielectrics, a.k.a. insulators. Both water and oil are dielectrics, and it turns out that the electrostatics of dielectrics explains why ions dissolve much better in water than in oil and therefore why ions do not easily pass through cell membranes in the absence of ion channels. More generally, electrostatics is tremendously important in biology as evidenced by the pH-dependence and ion concentration-dependence of living processes. However, understanding the character of electrostatic interactions in biology, where ionic solutions are ubiquitous, requires a synthesis to two key sets of ideas: Gauss’ Law, etc. from “classical electrostatics”, and the Boltzmann factor, etc. from statistical mechanics. We bring these two sets of concepts together, and show that for charges in ionic solution the long-ranged Coulomb interaction becomes a short-ranged, screened Coulomb interaction, which is ubiquitous in biology.

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• Published: 25 September 2023

Influence of electric potential-induced by atmospheric pressure plasma on cell response

• Takamasa Okumura 1 ,
• Chia-Hsing Chang 2 ,
• Kazunori Koga 1 ,
• Masaharu Shiratani 1 &
• Takehiko Sato 2  

Scientific Reports volume  13 , Article number:  15960 ( 2023 ) Cite this article

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• Plasma physics

Plasma irradiation leads not only active species, but also reactive chemical species, ultraviolet light, electric fields, magnetic fields, and shock waves. To date the effects of reactive chemical species have been mainly discussed. To understand the biological effect caused by an electric potential induced with an atmospheric-pressure plasma, the behavior of cell stimulated by electric potential was investigated using HeLa cell. The cell concentration assay revealed that less than 20% of cells inactivated by potential stimulation and the remained cells proliferate afterward. Fluorescent microscopic observation revealed that potential stimulation is appreciable to transport the molecules through membrane. These results show that potential stimulation induces intracellular and extracellular molecular transport, while the stimulation has a low lethal effect. A possible mechanism for this molecular transport by potential stimulation was also shown using numerical simulation based on an equivalent circuit of the experimental system including adhered HeLa cell. The potential formation caused by plasma generation is decisive in the contribution of plasma science to molecular biology and the elucidation of the mechanism underlying a biological response induction by plasma irradiation.

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Introduction.

Recently, atmospheric-pressure plasma has been intensively investigated for biomedical 1 , 2 , 3 , 4 , such as the inactivation of bacteria including antibiotic-resist germs, fungi, spores or viruses and the hemostasis 5 , 6 , 7 , 8 , and agricultural applications 9 , 10 , 11 , 12 , such as germination enhancement, subsequent growth improvement and DNA methylation alterations of plant seeds 13 , 14 , 15 . Hence, the plasma irradiation can be applied in medical and agricultural treatments. During the plasma irradiation, targets are covered with liquid phase and thus it is necessary to investigate the behavior of cells in liquid by plasma irradiation 16 .

A single biological effect of plasma-induced physical and chemical elements remains an important issue 17 . Although the plasma acts as a source of several active agents, e.g. , reactive chemical species, charged particles, ultraviolet light, electric fields, magnetic fields, and shock waves (Fig.  1 ) and one of these or combination induces a biological response 17 , 18 , 19 , the mechanism underlying the effects caused by the plasma has been discussed mainly in terms of reactive species to date. Recently, Chang et al . and his colleagues constructed the system to evaluate the effect of plasma-induced nanosecond pulsed current and chemical factors on human HT-1080 cells activities and observed a significant increase in cell migration along with altered cell morphology 19 , 20 , 21 , 22 . Mendis et al . theoretically discussed the mechanism underlying physical disruption of cell membranes due to plasma irradiation in terms of potential 23 . Furthermore, Yano et al . showed that pulsed electric field application at a low frequency range less than 1 MHz affects cell activity depending on the frequency 8 . Considering that the accumulated charge also has a biological effect in and of themselves 8 , 23 , the plasma-induced electric potential on living tissues is also crucial for the biological effects.

Plasma irradiation model for cells/tissues/organs.

To understand the biological effect of the electric potential of plasma, it is essential to exclude the influence of chemical species. We constructed a novel experimental system for cell stimulation that could physically isolate cells from reactive species generated at discharge region and thus allowed us to evaluate the direct effects of electrical potential fluctuation on cellular response. A possible mechanism for the cell response to potential stimulation was also shown using numerical simulation based on an equivalent circuit of the experimental system including adhered cell. Defining the interactions between the cell and the electric potential could help us understand the mechanisms complementary to biological effect induced by plasma irradiation. Our main goal was to investigate whether electrical potential affect cellular responses and provide the probable mechanism of the cell response.

Results and discussion

Discharge assessment assay of medium.

HeLa cell suspension in a culture medium was prepared in wells of a 96-well plate and incubated for 24 h, the cells were adhered to the bottom surface and used for potential stimulation as shown in Fig.  2 . The experimental parameters were listed in Table 1 . We prepared cells in two conditions; one experienced exposure to potential stimulation and the other was placed in the grounded medium (control). A pulsed discharge that propagates between the needle and the medium forms the potential in the liquid 24 , 25 . The potential fluctuation of the medium at the direct discharges was transferred through a SUS 316 cylindrical wire to the medium including HeLa cells. To generate plasma on the medium of direct plasma a pulsed voltage was applied to the needle electrode. Figure  3 shows typical waveforms of the applied voltage to the needle electrode and current flowing through the needle and the ground. Current spikes, corresponding to discharge occurrence, appeared with voltage changes. The first discharge occurs at 1.3 kV. The pulse width of the discharge current spikes are 88 ns, indicating that once a discharge propagates to the other side then it stops. These results show that discharge mode did not shift to arcing from streamer. The typical streamer channel is < 30 Td with the electron temperature T e  < 2.7 eV 26 . Such electrons mainly vibrationally excite N 2 and O 2 in the air and generate NO in the atmosphere 27 . Therefore, the media with cell were closed to prevent contamination of chemical species. If a discharge is generated in the medium with cell, the effect of potential stimulation on the cells cannot be extracted. When an electric discharge occurs, H 2 O 2 , relatively long-lived RONS, is generated in the medium by the chemical reaction through R1 and R2 28 .

where P is an energetic particle from the plasma (e.g., electron) and M is a collision partner (e.g., N 2 or O 2 ). Figure  4 shows H 2 O 2 concentration in the medium below the needle electrode (direct plasma), that of potential stimulation, and that of control after 60 min-plasma generation. H 2 O 2 concentration shows 0.67 ± 0.00 mg/L for direct plasma (n = 3). In contrast, H 2 O 2 was not detected in the medium with and without potential stimulation. When only one electrode with a certain potential is in contact with a liquid, the potential of the liquid is equipotential with the electrode and thus no discharge involving a chemical reaction occurs theoretically. This is consistent with the result in Fig.  4 . On the other hand, if consider hypothetically that the electrode immersed in the liquid has a high potential and plasma is generated, the discharge should be localized between the tip of the electrode and the liquid due to the concentration of the electric field 29 . In such early phenomenon, electrons use the region created by vaporization of liquid due to Joule heating to accelerate 29 . Note that in reference 29 the high voltage electrode and the ground electrode were placed in a liquid at a short distance. The region would be dominated by H 2 O and the chemical species produced in medium including cells would be dominated by *OH and hydrogen atom if the discharge occurs 29 , 30 Sato et al . also indicated that second positive and first negative band emissions of nitrogen were not detected in the region 29 . From the above, potential stimulation on HeLa cells will be discussed, excluding the effect of RONS. Additionally, H 2 O 2 is a chemical species that is a major contributor to the stress that cells undergo during plasma irradiation 31 . We preliminary found that nitrite HNO 2 has no inactivation effect up to concentrations of 2.5 mM (118 mg/L) and nitrate HNO 3 up to 5 mM (315 mg/L), H 2 O 2 even below 150 µM inactivates HeLa cells. This indicates that HNO 2 and HNO 3 , which are produced in large amounts by plasma irradiation in air gas to liquid, have relatively low toxicity to HeLa cells comparing to H 2 O 2 .

Experimental set-up.

Typical waveforms of the applied voltage to a needle electrode and current flowing between the needle electrode and the ground.

H 2 O 2 concentration of each medium for direct plasma, potential stimulation, and control. The duration of plasma irradiation was 60 min. N.D. shows not detected with a detection limit of 0.05 mg/L. The error bar of direct plasma is invisible due to the standard deviation was zero.

Cell concentration assay

The effect of potential stimulation on cells was evaluated by changes in the cell activity. Figure  5 shows changes in the concentration of living cells in the medium with and without potential stimulation for 30 min. The cell concentrations were measured after treatment (0 h) and after 24 h of incubation since the treatment (24 h). Figure  5 a was obtained after immediately (within 1–2 min after plasma irradiation) replacing the medium with phosphate-buffered saline (PBS) followed by cell concentration assay. The concentration of treated cells decreases in both 0 h and 24 h. Most cells remain active at 0 h after the treatment unless there is a steep disruption of cell membranes due to direct plasma irradiation. Notice that cell concentration was obtained by adding the reagent to the sample and incubating for 4 h according to the product protocol. Therefore, the possible mechanism of the decrease in cell concentration even at 0 h is due to a rapid cell inactivation during potential stimulation and a gradual cell inactivation during 4 h of incubation for assay. We evaluated %decrease due to potential stimulation by Eq. ( 1 ).

where n s is the concentration of living cell with potential stimulation (/mL) and n c is that without potential stimulation (/mL). In Fig.  5 ., %decrease is 85% at 0 h ( p  = 0.0055) and 86% at 24 h ( p  = 0.00099), respectively. HeLa cells adheres on the bottom using proteins such as extracellular matrix and adhesion molecules 32 . Local electric fields created by potential fluctuations might affect their protein function by changing its conformation 33 , 34 . Additionally, a global feature of plasma irradiation is instantaneous cell detachment from the bottom. I.E. Kieft et al. observed the detachment from the bottom for Chinese hamster ovary cells, an epithelial cell line, within a few minutes after a plasma irradiation for 5 s and the reattachment at 1 h after plasma irradiation 35 . Since the cell concentration of Fig.  5 a was obtained by replacing the medium with PBS immediately (within 1–2 min after plasma irradiation) after potential stimulation, the cells detached by potential stimulation might be discarded leading cell concentration decrease. Figure  5 b shows the concentration of cells counted after stimulation without replacing the medium with PBS. Nevertheless, %decrease was 84% ​​at 0 h ( p  = 0.012) and 84% at 24 h ( p  = 0.0033). This result is in good agreement with the result in Fig.  5 a. Consequently, potential stimulation affects the cells within 4 h at the longest after potential stimulation and these effects are not explained in terms of the detachment.

Cell concentration after a potential stimulation for 30 min ( a ) with and ( b ) without replacing medium with PBS. The time between stimulation treatment and measurement was 0 and 24 h. Initial cell concentration was 6.0 × 10 4 cell/mL in ( a ) and 1.0 × 10 5 cell/mL in ( b ). Statistical test of two tailed t -test was performed (* p  < 0.05, ** p  < 0.01, *** p  < 0.005, **** p  < 0.001). %Decrease was 85% for 0 h and 86% for 24 h in ( a ) and 86% for 0 h and 84% for 24 h in ( b ).

To discuss the subsequent effects, a proliferation ratio R p was obtained by Eq. ( 2 ).

where n 24h is the concentration of cells incubated for 24 h after potential stimulation and n 0h is that without incubation after potential stimulation. R p is 2.11 and 2.14 for control and stimulation in Fig.  5 a, and 2.61 and 2.55 in Fig.  5 b, respectively. Considering that the initial cell concentration was 6.0 × 10 4 cell/mL in Fig.  5 a and 1.0 × 10 5 cell/mL in Fig.  5 b, it is natural that Fig.  5 a shows higher cell proliferation ratios. However, it should be noted that the ratio is maintained at the same level as the control group, even though potential stimulation reduces the concentration of living cells. The cells may recover from temporal damage due to the stimulation. Considering that the doubling time of HeLa cells is within 24 h 36 , 37 , the cells may recover in a few hours after the stimulation. Alternatively, potential stimulation may shorten the cell cycle. The mechanism underlying how the cell proliferation rate is compensated (Fig.  5 ) should be clarified in the future. In this study, further experiments were conducted on the effects of potential fluctuations during plasma generation on cell membranes.

When a needle-liquid electric discharge occurs, an electric potential is formed in the liquid phase and requires more than several ten seconds to relax without ground 24 . Once potential is formed in medium including cell, the capacitors such as cell membrane and nuclei are charged depending on the voltage duration 38 , 39 , 40 . The voltage corresponds to the potential induced in a liquid medium by a pulsed discharge. A time difference between the first discharge and the subsequent discharge with a reverse polarity is 200 µs at maximum as shown in Fig.  3 . Assuming that the relaxation time of the cell membrane potential in the HeLa cell is about the same millisecond as that of the nerve cell 32 , the maximum potential is contentiously applied to inside and outside the cell for 200 µs. Considering that such a potential difference leads the transient mechanical compressive force due to Maxwell stress, perforation may occur on the cell membrane. To evaluate this, the influence of potential stimulation on the cell membrane was studied. We added membrane-impermeable fluorescent dye to the medium before and after the stimulation, and microscopically observed the fluorescence-stained cells. This approach allows us to estimate whether the perforations formed in the membrane are temporary or stationary.

Influence of potential stimulation on the cell membrane

Fluorescence microscopy observations revealed that potential stimulation causes temporal pores on the membrane through which fluorescent reagent transports into the living cells. Figure  6 shows the result of the microscopic fluorescent observation for the cells with and without stimulation. To elucidate the biological effect of plasma-induced potential stimulation, fluorescent regents MitoRed and SYTOX-Green in DMSO were added at (a) 0 h and (b) 24 h after potential stimulation for 30 min and (c) before the stimulation. In Fig.  6 a, cells were stained with MitoRed but not stained with SYTOX-Green. To quantitively evaluate the effect, the ratio of the number of cells simultaneously stained by both MitoRed and SYTOX-Green divided by the number of cells stained by MitoRed, GR ratio, were calculated. GR ratio enables us to assess the number of surviving cells with a non-lethal damage on the membrane. GR ratio was 0.097 in control group and 0.28 in stimulation group (Fig.  6 a; Table 2 ). After 24 h (Fig.  6 b), GR ratio was 0.12 in control group and 0.043 in stimulation group (Table 2 ). The number of MitoRed-stained cells with and without stimulation increased at almost the same, owing to proliferation. These results are consistent with Fig.  5 . Conversely, many cells were stained by SYTOX-Green when added at before stimulation, even they were also stained by MitoRed (Fig.  6 c). GR ratio was 0.16 in control group but 0.96 in stimulation group, which is significant high (Table 2 ). This result indicates that potential stimulation enables transport of SYTOX-Green into cells. It also should be noted that the cells with and without stimulation in Fig.  6 a and b were not stained by SYTOX-Green when the reagent added at 0 h and 24 h later since stimulation. These results suggest that potential stimulation make temporal pores on the membrane of HeLa cells. Further experiment was conducted to evaluate the molecular transport out of the cell. LDH level of each medium after cell exclusion with and without potential stimulation for 30 min was measured. LDH is a soluble cytoplasmic enzyme that is present in almost all cells and is released to the medium when the membrane is damaged due to pores formation 41 , 42 . The control showed high LDH levels at 1.115 ± 0.008 as shown in Fig.  7 . This is because phenol red and LDH that is originally contained in fetal bovine serum of the medium gives a positive bias to absorbance for colorimetry 43 . Nevertheless, potential stimulation shows slight but significant increase as 1.174 ± 0.045 than control ( p  = 0.021, n = 15). Above results show that potential stimulation induces molecular transport into and out of HeLa cell by temporal pores formation. This might be involved in the cell inactivation as shown in (Fig.  5 ). There are many reports on the formation of pores by atmospheric-pressure plasma irradiation to cells 44 , 45 , 46 , 47 , 48 . One of the mechanisms underlying pores formation is supplying plasma-induced radical species and other chemical species to the cell membrane, as Tero et al . have pointed out that lipid oxidation is involved in perforation 45 . This study revealed that potential simulation also has a key role for pores formation. It cannot be determined that all pores are reversible and thus there remains the possibility that the pores can be observed even after the treatment. Therefore, morphological change using SEM observations will be conducted in future.

Result of fluorescent microscopic observation (scale bar: 40 µm). The fluorescent regents were added different time at ( a ) 0 h and ( b ) 24 h after potential stimulation. In ( c ) the fluorescence reagents were added before the stimulation. Red and green correspond to living cells and cells with pore, respectively.

LDH level of each medium with and without potential stimulation for 30 min.

Possible mechanism underlying temporal poration by potential stimulation

Electric field across the membrane induced by the first discharge plasma (Fig.  3 ) was evaluated using LTspice XVII. Cell membrane potentials and continuous potential fluctuations between discharge current spikes were not addressed in this study. The discharge mode was the flashover 49 . As a result of the electron avalanche, the streamer shortens a circuit between the needle tip and the medium. The onset of the current spike and the start of the streamer propagation coincide in time. Based on a mean velocity of a streamer of 10 5  m/s and the distance between the needle tip and the medium was 1.5 mm, the time required for shortening the circuit is calculated to be 15 ns 50 . The applied voltage hardly changes in this time. Thus, the potential that generates the current spike is imparted to the liquid at the maximum. This allows us to propose a simple equivalent circuit composed of an upper membrane C m1 , a cytoplasm R c , a lower membrane C m2 of an adhered HeLa cell, bottom of polystyrene 96-well C b , blank space of 96-well plate (skirt) C s , and 200 mm space C a as shown in Fig.  8 a, where C is the capacitance and R is the resistance. These values ​​are calculated by Eqs. ( 3 – 4 ) as follows.

where \({\varepsilon }_{0}\) is electric constant as 8.854 × 10 −12 F/m, \({\varepsilon }_{\mathrm{r}}\) is relative permittivity, d is distance of the capacitor (m), ρ is resistivity (Ωm), derived by (3), l is the length (m), S is the cross-section area of the resister (m 2 ), and σ is the conductivity (mS/cm). C m1 and C m2 are both 9.929 × 10 −15 F, R c is 2.5 × 10 6 Ω, C b is 1.705 × 10 −20 F, C s is 6.542 × 10 −21 F, C a is 5.560 × 10 −23 F based on the physical characteristics as follows. For HeLa cell, \({\varepsilon }_{\mathrm{r}}\) of cell membrane is 6.25, derived by averaging 5.7 for erythrocyte and 6.8 for lymphocyte, d is 7 nm, σ of cytoplasm is 3.2 mS/cm, and vertical l of cytoplasm of an adhered HeLa cell on the well bottom is 1 µm 51 , 52 , 53 . Since the horizontal radius of the adhered HeLa cell is 40 µm 54 , an equivalent circuit was constructed in the smallest unit by assuming that the other elements except voltage source were regarded as the same radius as well as the adhered HeLa cell. Voltage source was set as a pulse mode with 1.3 kV for 200 µs based on Fig.  3 . For the 96-well plate, \({\varepsilon }_{\mathrm{r}}\) of polystyrene is 2.3 55 , d of bottom is 1.5 mm according to the product manufacturer. \({\varepsilon }_{\mathrm{r}}\) of air is 1.0. Figure  8 b shows the simulation result. An applied voltage shows the potential of the medium with cell. V m1 and V m2 show the voltage across the upper and the lower membrane, respectively. The voltage applied to the membrane is divided depending on each capacitance. As shown in Fig.  8 b as the current charges the capacitors, V m1 and V m2 gradually increase and reach 53 V and 27 V at 200 µs. The electric field was calculated as 7.6 × 10 3  kV/mm for the upper membrane and 3.9 × 10 3  kV/mm for the lower membrane. It is obvious that the electric field intensity decreases with a comprehensive equivalent circuit including all the intracellular components and more advanced components such as a membrane with channels and transporters. It should be noted that the simulation result also shows that a larger electric field is applied to the upper cell membrane, comparing to the lower cell membrane, i.e., perforation may occur in the upper cell membrane. Deng et al . applied 6.0 kV of pulsed voltage between parallel plates inserted into a cell suspension at a distance of 1 cm and observed cell morphology after 15 min 38 . The cell morphology did not change as pulse width at 10 µs. In contrast, the cell membrane partially collapsed as that at 100 µs 38 . For this study, the electric field is maintained up to 200 µs. It was experimentally and theoretically shown that the potential induced in the liquid phase during plasma irradiation has a reversible perforation effect on the HeLa cell membrane. Plasma irradiation could be used to efficiently transport the generated RONS and other target molecules into cells.

Numerical simulation using LTspice XVII. ( a ) Proposed equivalent circuit and ( b ) voltage and current.

Conclusions

In this study, we investigated the biological effects of potential formation in the culture medium and cytoplasm induced by plasma irradiation on cells using cell activity, microscopic fluorescence observations, and a numerical simulation. A gas–liquid interfacial discharge plasma was generated by a bipolar pulse voltage, and only the potential fluctuation stimulus was given to the medium in which the cells were present. 30 min of electrical potential stimulation reduced the number of viable cells by about 85%. However, the cell proliferation rate after 24 h incubation was 2.1, which was almost the same as that of cells without stimulation. These results indicate that cells that remain active under potential stimulation can normally proliferate. Fluorescence microscopy has shown that fluorescent molecules that are impermeable to no-damaged cell membranes are transported into cells by potential stimulation. This was not observed when the fluorescent molecule is added after potential stimulation. Consequently, potential stimulation induces temporal perforation in the cell membrane. LDH measurement in the supernatant supports this result and suggests that potential stimulation can transport molecules in and out of cells. The numerical simulation on a transient analysis based on the physical properties of previous research and the actual applied voltage in this study showed that a larger electric field is induced inside and outside the upper membrane of HeLa cells adhering to the bottom than the lower membrane. In summary, we concluded that the mechanism underlying the potential-stimulated intracellular and extracellular molecular transport is primary pore formation on the upper membrane of HeLa cells. This study is the first report on the molecular transport into and out of cells by the potential formed in the liquid phase when irradiating a living cells with plasma. The potential fluctuation stimulation associated with plasma irradiation is a highly efficient molecular transport technology that does not inhibit cell proliferation, so it can be expected to be applied to medical treatment and agriculture. Transporting molecules into cells while maintaining cell activity is continuously required in fields such as regenerative medicine. The potential formation caused by plasma generation is decisive in the contribution of plasma science to cell biology and the elucidation of the mechanism underlying a biological response induction by plasma irradiation.

HeLa cell preparation

The HeLa cells was provided from Cell Resource Center for Biomedical Research, Institute of Development, Aging and Cancer, Tohoku University. HeLa cells were cultured in a culture medium composed of a regular medium which consists of minimum essential medium (MEM; Sigma, M4655-500) with 10% fetal bovine serum (FBS; Invitrogen 10437077) and 2% penicillin–Streptomycin mixed solution (Penicillin 10,000 µg/mL; Nacalai Tesque 26253-84). The electric conductivity of the culture medium was 9.53 mS/cm. We adjusted cell suspensions at 6.0 × 10 4 –1.0 × 10 5 cell/mL using and prepared 100 μL/well in 96-well plate (Iwaki, 3861-096). After 24 h of incubation at 37 °C with 5% CO 2 , the cells were used for subsequent evaluation.

Potential stimulation

Figure  2 shows the experimental set-up. As shown in the figure, two conditions of cells were prepared in a 96-well plate made of insulating material in a clean bench to prevent bacterial contamination. One experienced exposure to potential stimulation and the other was placed in the grounded medium (control). The distance between a needle tip and a medium's surface was 1.5 mm. A pulsed voltage with an amplitude of ± 7.5 kV, a rise time of 8 μs, width of 9 μs and 5 kpps of pulse repetition rate was applied for 30 or 60 min to the needle electrode by a function generator (NF, WF1973) and a high voltage amplifier (Trek, PD05034). Large current was prevented by insertion of dielectric material between the medium under the needle electrode and the ground. The potential fluctuation of medium to which direct discharges were generated was transferred through a SUS 316 cylindrical wire to the medium including HeLa cells. The tip of the cylindrical wire was submerged to a depth of 1 mm. During the treatment, the 96-well plate was placed 200 mm away from the ground to prevent the plasma generation at the bottom.

Hydrogen peroxide assay

The H 2 O 2 concentration of the medium was measured by colorimetry using a MEM eagle (GIBCO, 51200-038), instead of the MEM with phenol red, pack test reagent (Kyoritsu, WAK-H 2 O 2 ) and digital pack test-Multi SP (Kyoritsu, DPM-MT). The limit of detection (LOD) was 0.05 mg/L. The conductivity of the medium including MEM eagle was 9.36 mS/cm.

Cell concentration

The survival cell concentration was measured by cell count reagent SF (Nakarai tesque; 10% in the regular medium) and a microplate reader (Thermo Scientific, Multiskan FC) with the product protocol. The reagent was added to the sample and analyzed after an incubation for 4 h. See Fig. S1 in supporting information for the standard curve used in this study.

Fluorescence microscopy

Fluorescence microscopy was used to elucidate the biological effect of plasma-induced potential stimulation using fluorescent regents MitoRed (Dojindo, 344-08851) and SYTOX-Green (Thermo, S7020). MitoRed stains living cells and SYTOX-Green stains cells with pores on their membrane. Both fluorescent reagents were simultaneously used to count surviving cells with damage on the membrane. The fluorescence reagents were added at different times, 0 h and 24 h after potential stimulation, and before the stimulation. The fluorescence images of the HeLa cells were taken by an inverted fluorescence microscope (Carl Zeiss, Axio Observer D1) using a 96-well glass bottom plate (Iwaki, 5866-096).

Cell membrane response to potential stimulation

The damage to the cell membrane by potential stimulation was assessed by measuring lactate dehydrogenase (LDH) enzyme activity released into the medium using LDH Cytotoxicity Detection Kit (Takara, MK401) and a microplate reader with the product protocol. After potential stimulation, 80 µL of the supernatant and 40 µL of LDH assay reagent were mixed and incubated for 30 min in a 96-well. The absorbance of the samples was measured at 492 nm. The reference wavelength was 620 nm.

Numerical simulation

A numerical simulation of the proposed equivalent circuit of an experimental system including an adhered HeLa cell was performed using LTspice XVII 56 to assess the voltage across the membrane as the exposure to potential stimulation. The physical characteristics of the electrical elements are shown in the section of results and discussions.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the Collaborative Research Project of the Institute of Fluid Science, Tohoku University, Japan; J19I089. This work was partially supported by Japan Society of the Promotion of Science (JSPS)-KAKENHI Grant Number JP20H01893, JP19K14700, JP22K03586, and JP19H05462.

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T.O., and T.S. designed the study, prepared, and characterized samples, and wrote the manuscripts. T.O. and C.C. performed experiments. T.O., K. K., M.S. and T.S. discussed the results and the manuscript including revisions.

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Okumura, T., Chang, CH., Koga, K. et al. Influence of electric potential-induced by atmospheric pressure plasma on cell response. Sci Rep 13 , 15960 (2023). https://doi.org/10.1038/s41598-023-42976-4

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In a hydrogen-generating electrolyzer, this approach is used to remove protons from water and add electrons to the protons to form hydrogen gas. In a fuel cell, electricity is generated when protons and electrons are removed from hydrogen gas and added to oxygen to form water.

Proton-coupled electron transfer is common in many other types of chemical reactions, for example, carbon dioxide reduction (the conversion of carbon dioxide into chemical fuels by adding electrons and protons). Scientists have learned a great deal about how these reactions occur when the proton acceptors are molecules, because they can precisely control the structure of each molecule and observe how electrons and protons pass between them. However, when proton-coupled electron transfer occurs at the surface of an electrode, the process is much more difficult to study because electrode surfaces are usually very heterogenous, with many different sites that a proton could potentially bind to.

To overcome that obstacle, the MIT team developed a way to design electrode surfaces that gives them much more precise control over the composition of the electrode surface. Their electrodes consist of sheets of graphene with organic, ring-containing compounds attached to the surface. At the end of each of these organic molecules is a negatively charged oxygen ion that can accept protons from the surrounding solution, which causes an electron to flow from the circuit into the graphitic surface.

“We can create an electrode that doesn’t consist of a wide diversity of sites but is a uniform array of a single type of very well-defined sites that can each bind a proton with the same affinity,” Surendranath says. “Since we have these very well-defined sites, what this allowed us to do was really unravel the kinetics of these processes.”

Using this system, the researchers were able to measure the flow of electrical current to the electrodes, which allowed them to calculate the rate of proton transfer to the oxygen ion at the surface at equilibrium — the state when the rates of proton donation to the surface and proton transfer back to solution from the surface are equal. They found that the pH of the surrounding solution has a significant effect on this rate: The highest rates occurred at the extreme ends of the pH scale — pH 0, the most acidic, and pH 14, the most basic.

To explain these results, researchers developed a model based on two possible reactions that can occur at the electrode. In the first, hydronium ions (H 3 O + ), which are in high concentration in strongly acidic solutions, deliver protons to the surface oxygen ions, generating water. In the second, water delivers protons to the surface oxygen ions, generating hydroxide ions (OH - ), which are in high concentration in strongly basic solutions.

However, the rate at pH 0 is about four times faster than the rate at pH 14, in part because hydronium gives up protons at a faster rate than water.

A reaction to reconsider

The researchers also discovered, to their surprise, that the two reactions have equal rates not at neutral pH 7, where hydronium and hydroxide concentrations are equal, but at pH 10, where the concentration of hydroxide ions is 1 million times that of hydronium. The model suggests this is because the forward reaction involving proton donation from hydronium or water contributes more to the overall rate than the backward reaction involving proton removal by water or hydroxide.

Existing models of how these reactions occur at electrode surfaces assume that the forward and backward reactions contribute equally to the overall rate, so the new findings suggest that those models may need to be reconsidered, the researchers say.

“That’s the default assumption, that the forward and reverse reactions contribute equally to the reaction rate,” Surendranath says. “Our finding is really eye-opening because it means that the assumption that people are using to analyze everything from fuel cell catalysis to hydrogen evolution may be something we need to revisit.”

The researchers are now using their experimental setup to study how adding different types of ions to the electrolyte solution surrounding the electrode may speed up or slow down the rate of proton-coupled electron flow.

“With our system, we know that our sites are constant and not affecting each other, so we can read out what the change in the solution is doing to the reaction at the surface,” Lewis says.

The research was funded by the U.S. Department of Energy Office of Basic Energy Sciences.

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NASA Discovers a Long-Sought Global Electric Field on Earth

• A rocket team reports the first successful detection of Earth’s ambipolar electric field: a weak, planet-wide electric field as fundamental as Earth’s gravity and magnetic fields.
• First hypothesized more than 60 years ago, the ambipolar electric field is a key driver of the “polar wind,” a steady outflow of charged particles into space that occurs above Earth’s poles.
• This electric field lifts charged particles in our upper atmosphere to greater heights than they would otherwise reach and may have shaped our planet’s evolution in ways yet to be explored.

Using observations from a NASA suborbital rocket, an international team of scientists has, for the first time, successfully measured a planet-wide electric field thought to be as fundamental to Earth as its gravity and magnetic fields. Known as the ambipolar electric field, scientists first hypothesized over 60 years ago that it drove how our planet’s atmosphere can escape above Earth’s North and South Poles. Measurements from the rocket, NASA’s Endurance mission , have confirmed the existence of the ambipolar field and quantified its strength, revealing its role in driving atmospheric escape and shaping our ionosphere — a layer of the upper atmosphere — more broadly.

Understanding the complex movements and evolution of our planet’s atmosphere provides clues not only to the history of Earth but also gives us insight into the mysteries of other planets and determining which ones might be hospitable to life. The paper was published Wednesday, Aug. 28, 2024, in the journal Nature .

An Electric Field Drawing Particles Out to Space

Since the late 1960s, spacecraft flying over Earth’s poles have detected a stream of particles flowing from our atmosphere into space. Theorists predicted this outflow, which they dubbed the “polar wind,” spurring research to understand its causes. 

Some amount of outflow from our atmosphere was expected. Intense, unfiltered sunlight should cause some particles from our air to escape into space, like steam evaporating from a pot of water. But the observed polar wind was more mysterious. Many particles within it were cold, with no signs they had been heated — yet they were traveling at supersonic speeds.

“Something had to be drawing these particles out of the atmosphere,” said Glyn Collinson, principal investigator of Endurance at NASA’s Goddard Space Flight Center in Greenbelt, Maryland, and lead author of the paper. Scientists suspected a yet-to-be-discovered electric field could be at work.

The hypothesized electric field, generated at the subatomic scale, was expected to be incredibly weak, with its effects felt only over hundreds of miles. For decades, detecting it was beyond the limits of existing technology. In 2016, Collinson and his team got to work inventing a new instrument they thought was up to the task of measuring Earth’s ambipolar field.

How the Ambipolar Field Works

A weak electric field in the upper atmosphere may loft charged particles into space..

Scientists theorized this electric field should begin at around 150 miles (250 kilometers) altitude, where atoms in our atmosphere break apart into negatively charged electrons and positively charged ions. Electrons are incredibly light — the slightest kick of energy could send them shooting out to space. Ions are at least 1,836 times heavier and tend to sink toward the ground. If gravity alone were in play, the two populations, once separated, would drift apart over time. But given their opposite electric charges, an electric field forms to tether them together, preventing any separation of charges and counteracting some of the effects of gravity.

This electric field is bidirectional, or “ambipolar,” because it works in both directions. Ions pull the electrons down with them as they sink with gravity. At the same time, electrons lift ions to greater heights as they attempt to escape to space, like a tiny dog tugging on its sluggish owner’s leash. The net effect of the ambipolar field is to extend the height of the atmosphere, lifting some ions high enough to escape with the polar wind. Animation credits: NASA/Conceptual Image Lab/Wes Buchanan/Krystofer Kim

Launching a Rocket from the Arctic

The team’s instruments and ideas were best suited for a suborbital rocket flight launched from the Arctic. In a nod to the ship that carried Ernest Shackleton on his famous 1914 voyage to Antarctica, the team named their mission Endurance. The scientists set a course for Svalbard, a Norwegian archipelago just a few hundred miles from the North Pole and home to the northernmost rocket range in the world.

“Svalbard is the only rocket range in the world where you can fly through the polar wind and make the measurements we needed,” said Suzie Imber, a space physicist at the University of Leicester, UK, and co-author of the paper.

On May 11, 2022, Endurance launched and reached an altitude of 477.23 miles (768.03 kilometers), splashing down 19 minutes later in the Greenland Sea. Across the 322-mile altitude range where it collected data, Endurance measured a change in electric potential of only 0.55 volts.

“A half a volt is almost nothing — it’s only about as strong as a watch battery,” Collinson said. “But that’s just the right amount to explain the polar wind.”

Hydrogen ions, the most abundant type of particle in the polar wind, experience an outward force from this field 10.6 times stronger than gravity. “That’s more than enough to counter gravity — in fact, it’s enough to launch them upwards into space at supersonic speeds,” said Alex Glocer, Endurance project scientist at NASA Goddard and co-author of the paper.

Heavier particles also get a boost. Oxygen ions at that same altitude, immersed in this half-a-volt field, weigh half as much. In general, the team found that the ambipolar field increases what’s known as the “scale height” of the ionosphere by 271%, meaning the ionosphere remains denser to greater heights than it would be without it.

“It’s like this conveyor belt, lifting the atmosphere up into space,” Collinson added.

Endurance’s discovery has opened many new paths for exploration. The ambipolar field, as a fundamental energy field of our planet alongside gravity and magnetism, may have continuously shaped the evolution of our atmosphere in ways we can now begin to explore. Because it’s created by the internal dynamics of an atmosphere, similar electric fields are expected to exist on other planets, including Venus and Mars.

“Any planet with an atmosphere should have an ambipolar field,” Collinson said. “Now that we’ve finally measured it, we can begin learning how it’s shaped our planet as well as others over time.”

By Miles Hatfield and Rachel Lense NASA’s Goddard Space Flight Center, Greenbelt, Md. Media Contact: Sarah Frazier, [email protected]

Endurance was a NASA-funded mission conducted through the Sounding Rocket Program at NASA’s Wallops Flight Facility in Virginia. The Svalbard Rocket Range is owned and operated by Andøya Space. The European Incoherent Scatter Scientific Association (EISCAT) Svalbard radar, located in Longyearbyen, made ground-based measurements of the ionosphere critical to interpreting the rocket data. The United Kingdom Natural Environment Research Council (NERC) and the Research Council of Norway (RCN) funded the EISCAT radar for the Endurance mission. EISCAT is owned and operated by research institutes and research councils of Norway, Sweden, Finland, Japan, China, and the United Kingdom (the EISCAT Associates). The Endurance mission team encompasses affiliates of the Catholic University of America, Embry-Riddle Aeronautical University, the University of California, Berkeley, the University of Colorado at Boulder, the University of Leicester, U.K., the University of New Hampshire, and Penn State University.

Related Terms

• Goddard Space Flight Center
• Heliophysics
• Heliophysics Division
• Science & Research
• Sounding Rockets
• Sounding Rockets Program

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Electric fields boost graphene's potential, study shows

by University of Manchester

Researchers at the National Graphene Institute have made a discovery that could revolutionize energy harnessing and information computing. Their study, published in Nature , reveals how electric field effects can selectively accelerate coupled electrochemical processes in graphene.

Electrochemical processes are essential in renewable energy technologies like batteries, fuel cells, and electrolyzers. However, their efficiency is often hindered by slow reactions and unwanted side effects. Traditional approaches have focused on new materials, yet significant challenges remain.

The Manchester team, led by Dr. Marcelo Lozada-Hidalgo, has taken a novel approach. They have successfully decoupled the inseparable link between charge and electric field within graphene electrodes, enabling unprecedented control over electrochemical processes in this material. The breakthrough challenges previous assumptions and opens new avenues for energy technologies.

Dr. Lozada-Hidalgo sees this discovery as transformative and said, "We've managed to open up a previously inaccessible parameter space. A way to visualize this is to imagine a field in the countryside with hills and valleys. Classically, for a given system and a given catalyst, an electrochemical process would run through a set path through this field.

"If the path goes through a high hill or a deep valley—bad luck. Our work shows that, at least for the processes we investigated here, we have access to the whole field. If there is a hill or valley we do not want to go to, we can avoid it."

The study focuses on proton-related processes fundamental for hydrogen catalysts and electronic devices. Specifically, the team examined two proton processes in graphene:

• Proton transmission: This process is important for developing new hydrogen catalysts and fuel cell membranes.
• Proton adsorption (Hydrogenation): Important for electronic devices like transistors, this process switches graphene's conductivity on and off.

Traditionally, these processes were coupled in graphene devices, making it challenging to control one without impacting the other. The researchers managed to decouple these processes, finding that electric field effects could significantly accelerate proton transmission while independently driving hydrogenation. This selective acceleration was unexpected and presents a new method to drive electrochemical processes.

Highlighting the broader implications in energy applications, Dr. Jincheng Tong, first author of the paper, said, "We demonstrate that electric field effects can disentangle and accelerate electrochemical processes in 2D crystals. This could be combined with state-of-the-art catalysts to efficiently drive complex processes like CO 2 reduction, which remain enormous societal challenges."

Dr. Yangming Fu, co-first author, pointed to potential applications in computing and said, "Control of these processes gives our graphene devices dual functionality as both memory and logic gate. This paves the way for new computing networks that operate with protons. This could enable compact, low-energy analog computing devices."

Journal information: Nature

Provided by University of Manchester

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It’s 2024 and now bicycle hackers can shift your gears.

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Security researchers find critical vulnerabilities in wireless bicycle gears

You may not ride an electric bicycle but that doesn’t mean you are safe from hackers. Security researchers have revealed critical vulnerabilities that can enable a hacker to take control of the latest gear-shifting technology, changing or jamming gears from as far as 32 feet away.

In their MakeShift: Security Analysis of Shimano Di2 Wireless Gear Shifting in Bicycles research paper presented during the WOOT Conference on Offensive Technologies earlier this month, Maryam Motallebighomi, Aanjhan Ranganathan from Northeastern University and Earlence Fernandes from UC San Diego, address the potential security issues surrounding the use of wireless gear-shifting technology in modern bicycles.

Modern Bicycles Increasingly Contain Tech That’s Vulnerable To Hackers

The bicycle industry, especially at the professional or racing end of the spectrum, is increasingly adopting the use of embedded computers and wireless technology. This is especially the case when it comes to gear-shifting tech that can offer highly valuable time advantages when it comes to racing performance. The trio of security researchers used what’s known as a blackbox analysis to uncover a number of critical vulnerabilities in one of the market-leading providers of such kit. Focusing on Shimano Di2 wireless gear-shifting technology, the researchers said they were able to find the following three vulnerabilities:

• A lack of preventative mechanisms when it comes to executing replay attacks that could enable a hacker to both capture and then re-transmit gear shift commands.
• The ability to execute targeted jamming enabling an attacker to disable gear-shifts completely on a target bicycle.
• Information leakage in the wireless communications protocol stack allowing telemetry from the bike to be analysed by an attacker.

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By exploiting these vulnerabilities, the researchers said, it was possible to control the gears without any need for cryptographic keys, from a distance of 32 feet, using simple software-defined radios. It would also be possible to jam the gears completely for a specific bike, say one in a peloton of cyclists during a race, without impacting the other riders.

Digital systems have many advantages over traditional mechanical ones, not least the responsiveness of gear shifts and the customization of these. Wireless gear-shifting employs, as you would expect, wireless links between gear shifters and the electro-mechanical derailleur using motors to move the chain between gears.

“Any security vulnerability in this system can significantly impact the rider’s safety and performance,” the researchers said, “especially in professional bike races, where an attacker could target a victim rider to gain an unfair competitive advantage.”

More Than An Inconvenience, Gear Jamming Could Be Highly Dangerous

While the ability to change gears remotely may sound like a bit of harmful fun, causing your mate to work harder going up a hill, the potential for harm is not to be underestimated. Take the example of a professional racing event with dozens, if not hundreds, of cyclists packed close together and reaching high speeds. “If an attacker were to target a subset of riders and shift the gears or jam the shifting operation,” the researchers warn, “it could result in crashes and injuries.”

To demonstrate the vulnerabilities, the researchers were able to use a simple software-defined radio and a standard laptop. Further development could easily shrink the size of the attack equipment to something portable and relatively easy to conceal.

Mitigating The Dangers Of Bicycle Hacking Attacks

The researchers suggested a number of mitigations that could be used to prevent such attacks. Such things as adding timestamps into the wireless communications, although this is far from straightforward in a scenario where GPS or internet signals are required for precise synchronization. Rolling codes are another mitigation, as is the use of some kind of distance-based restriction between shifters and derailleurs.

I reached out to Shimano for a statement and it is published here in full:

"Thanks for your inquiry about Shimano wireless shifting and the recent information shared by researchers regarding cybersecurity of the Di2 shifting platform. Shimano has indeed been working with researchers to enhance Di2 wireless communication security for all riders. Through this collaboration, Shimano engineers identified and created a new firmware update to enhance the security of the Di2 wireless communication systems.

We cannot share details on the exact fix at this moment for obvious security reasons. However, we can share that this update is intended to improve wireless transmission across Shimano Di2 component platforms and continue providing the highest level of shifting performance for which Shimano is renowned.

The firmware update has already been provided to our professional race teams and will be available for all riders in late August. With this release, riders can perform a firmware update on the rear derailleur using Shimano’s E-TUBE Cyclist smartphone app. More information about this process and steps riders can take to update their Di2 systems will be available shortly."

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