# What is Electric potential: Definition and 1000 Discussions

The electric potential (also called the electric field potential, potential drop, the electrostatic potential) is the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field with negligible acceleration of the test charge to avoid producing kinetic energy or radiation by test charge. Typically, the reference point is the Earth or a point at infinity, although any point can be used. More precisely it is the energy per unit charge for a small test charge that does not disturb significantly the field and the charge distribution producing the field under consideration.
In classical electrostatics, the electrostatic field is a vector quantity which is expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ, equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured in coulombs). By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself. In short, electric potential is the electric potential energy per unit charge.
This value can be calculated in either a static (time-invariant) or a dynamic (varying with time) electric field at a specific time in units of joules per coulomb (J⋅C−1), or volts (V). The electric potential at infinity is assumed to be zero.
In electrodynamics, when time-varying fields are present, the electric field cannot be expressed only in terms of a scalar potential. Instead, the electric field can be expressed in terms of both the scalar electric potential and the magnetic vector potential. The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.
Practically, electric potential is always a continuous function in space; Otherwise, the spatial derivative of it will yield a field with infinite magnitude, which is practically impossible. Even an idealized point charge has 1 ⁄ r potential, which is continuous everywhere except the origin. The electric field is not continuous across an idealized surface charge, but it is not infinite at any point. Therefore, the electric potential is continuous across an idealized surface charge. An idealized linear charge has ln(r) potential, which is continuous everywhere except on the linear charge.

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1. ### I Video: 'How electricity actually works'

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2. ### I Electric Potential in circuit

I reviewed some of the fundamental physics and I looked back at the equation for Electric potential at a point p: $$V(p) = k \sum_{i} {\frac {q_i} {r_i}}$$ where - p is the point at which the potential is evaluated; - ri is the distance between point p and point i at which there is a nonzero...
3. ### Potential and Electric Field near a Charged CD Disk

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4. ### Why Is the Electric Potential the Same for Inner and Outer Semi-Circles?

I solved using the formulae listed in the relevant equations and got the right answer. However, I noticed something strange to me. The electric potential due to the inner semi-circle was equal to that due to the outer semi-circle. But based on the formula for calculating V, we notice that there...
5. ### Two different dielectrics between parallel-plate capacitor

We have a parallel plate capacitor with two different dielectrics It seems to be the case that the potential difference on each half of the capacitor is the same. Initially, the electric field was ##\vec{E_0}=\frac{2\sigma_+}{\epsilon_0}\hat{j}##. If we were to insert a single dielectric...
6. ### Finding electric potential of an infinite line charge at z axis

The question says: Find the electric potential of the infinite line charge at ##\Phi \left(x,y\right)##, when known ##\Phi \left(0,0\right)=0## I am having hard time finding the electric potential of such. We know that the line charge is infinite at Z axis. And we know ##\Phi...
7. ### I Electric potential and potential difference

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8. ### MIT OCW, 8.02 Electromagnetism: Potential for an Electric Dipole

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9. ### Calculating Distance Travelled Using Electric Potential

I only could calculate the distance travelled by each body, by making the difference between the initial and final electric potential work equal to the work of friction done by the 2 bodies.
10. ### Work of the electric potential

I tried to make the kinetic energy of the first electron equal to the electric potential work. mv^2/2=ke^2/d We have to solve for the minimum distance between them: d=2ke^2/mv^2=5.05*10^-10 m The force is: F=ke^2/d^2=9*10^-10 N, which is not correct.
11. ### I Grounded Means Zero Electric Potential: Exploring the Method of Images

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12. ### Calculating Electric Potential for a Non-Negligible Thickness Toroid

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13. ### Graphing electric potential for two positive charges

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14. ### Why do we have a charge in the denominator of equation for voltage?

Why do we have a charge in the denominator of equations for voltage and el. potential if both voltage and el. potential are not dependent on charge? Is it just because that was the only way to derive the formula for voltage and then we realized we don't need q? U=W/q --> U=eqd/q.
15. ### Electric Potential of a Sphere: A Puzzling Problem

I can calculate the electric field strength at any point above the plane with Gauss' Law (##E = \frac{\eta}{\varepsilon_0}##) and so the electric potential at any point a perpendicular distance ##z## above the conducting plane (##V=−\frac{\eta}{\varepsilon_0}z##). But I'm having trouble taking...
16. ### Electric Potential Field Calculation

I've already tried to calculate the potential with respect to the 3 segments and then apply superposition (V1+V2+V3). However, I was not very successful. My error I think is in the calculation of the radii, mainly of the line segment that is on the z axis. Can anybody help me? I need some light...
17. ### Problem about electric potential

Can anyone help me how to solve this problem ?! I am sure that my answer is not right :
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19. ### Potential on the axis of a uniformly charged ring

We know that $$V_Z=\int_{\textrm{ring}} E\cdot dl$$ We therefore consider ##E=\dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r##. Then, $$V_Z=\int_{\textrm{ring}} \dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r\, dl = \dfrac{\lambda}{2\pi \varepsilon_0}\dfrac1r \int_{\textrm{ring}}dl=$$...
20. ### Electric Potential Difference -- Conceptual Question

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21. ### Work to bring a charge to the center of two quarter circles

By measuring angle \theta from the positive ##x## axis counterclockwise as usual, I get ##d\vec{E}=k( (\lambda_2-\lambda_1)\cos(\theta)d\theta, (\lambda_2-\lambda_1)\sin(\theta)d\theta )## and by integrating from ##\theta=0## to ##\theta=\frac{\pi}{2}## I get...
22. ### The electric field from its electric potential: semicircle

According to theory I should be able to get the Electric Field (E) from its pOtential (V) by doing the grad (V) so E = -grad(V), however, V is contant V = k*lambda* pi which results having E =0, but this is not right. What I am missing?? see figure below The answer should be Ex = 2*k*lambda / r...
23. ### Relationship between E and V in space

(a) Knowing ##E##, we can use equation (2) to determine ##V##. However, since ##\vec E## represents the distribution of electric field in space i.e. a function of (x,y,z). For example, ##\vec E = x \hat i + y \hat j + z \hat k##. Here we do not know this function so how can we know ##V## at a...
24. ### Does work = neg or pos change in potential energy?

u = (9*10^9)(1.61*10^-19)^2 * (1/[3*10^-15 ]- 1/[2*10^-10]) u = 7.68*10^-14 J but here the question. I have been taught that W= -U so shouldn't the answer be negative?? When i look up at the solution all other sources say that the W = U and therefore the answer is in postive.
25. ### I Electric Potential -- Is my understanding correct?

I have been having a hard time understanding Electric Potential and believe I finally have a grasp on what is trying to say. I wanted to right out my understanding here and hopefully have someone confirm what I am saying is somewhat accurate as I feel like when you write stuff out you tend to...
26. ### Potential Energy of three charged particles

I set up an equation for the sum of all the potential energies and when cancelling out ##k## and ##q^2##, I got ##\frac{1}{0.05}-\frac{1}{x}-\frac{1}{0.05-x}=0##. However, this has no solutions, so I must've gone wrong somewhere. Could someone just give me a hint, not a solution, that would put...
27. ### I What's the electric potential of the Earth?

I was wondering, we constantly assume the reference of zero potential is the surface of the Earth. But if we consider the reference to be the infinity, what would be the electric potential of the Earth? As Faraday says, the Earth is charged with a -580 kC of negative charge. If we consider...
28. ### What's wrong? Electric potential of a point on a ring

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30. E

### I Co-rotating electric potential for KN solution

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31. ### Electric potential inside a hollow sphere with non-uniform charge

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32. ### Electric Potential of point outside cylinder

Edit: Below is my work but i believe i have chosen the wrong values of the separation vector in the s direction. Any ideas as to what it should be?
33. ### Calculating the force on an electron from two positive point charges

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34. ### Potential Gradient for individual charges and parallel plates?

In my book, the potential gradient for a charge placed anywhere in space is defined as: E = -V/r HOWEVER, for parallel plate (capacitors) the potential gradient is defined as E = V/d (V being the potential difference). How come there's no negative sign for the potential gradient of the parallel...

36. ### Deriving electric and vector potential

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37. ### Who invented electric potential and why?

Why was that concept necessary ?, I know there's also a gravitational equivalent of this concept I couldn't find anything on google Thanks Daniel
38. ### Electrostatics - electric potential and field strength (dielectric)

Could somebody check my solution?
39. ### Final electric potential difference in a circuit with two capacitors

So, each capacitor must have a different potential difference, given by its capacity and charge... this would cause charge and current accordingly to flow in the circuit. But how do I determine the final potential difference, which would of course be the same for both of them? I have tried...
40. ### Electrostatic - electric potential due to a point charge

Could somebody check my solution? I want to know is it correct.
41. ### Electric potential difference at the ends of a resistor

So, having two parallel resistor ##R_{1}## and ##R_{2}## , the current flowing through the equivalent one will be ##I_{eq}=I_{1}+I_{2}##. Now, it comes the point I'm not totally getting: why is ##V_{eq}=V_{1}=V_{2}##? These V's are the difference of potential measured between which points...
42. ### Clarifications about electric potential and potential difference

Specifically, I haven't really got all the "methods" through which you could calculate or derive the electric potential and in some situations, I cannot understand how and when to apply this concept. Is it something caused by any charge, or must there be an interaction between the two to...
43. ### Finding the Monopole and Multipole Moments of the Electric Potential

My first attempt revolved mostly around the solution method shown in this "site" or PowerPoint: http://physics.gmu.edu/~joe/PHYS685/Topic4.pdf . However, after studying the content and writing down my answer for the monopole moment as equal to ##\sqrt{\frac{1}{4 \pi}} \rho##, I found out the...
44. ### Electric Potential Energy Question: Electron and Proton accelerating between charged plates

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45. ### Electric Potential inside an insulating sphere

I used the potential at the surface of the sphere for my reference point for computing the potential at a point r < R in the sphere. The potential at the surface of the sphere is ## V(R) = k \frac {Q} {R} ##. To find the potential inside the sphere, I used the Electric field inside of an...
46. ### Voltage using different references

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47. ### Does potential drop when a charge flows through a wire w/ 0 resistance?

Let us connect a battery of potential difference V to a wire. There is no resistance. Nothing! Now the battery creates some potential difference and the charges in the conducting wire move due to the Electric field created in the conductor by the battery. So, as the charge moves, its potential...
48. ### Charge rearrangement on conducting spheres

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