# Electric potential Definition and 120 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. ### 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.
2. ### 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, $$V_Z=\int_{\textrm{ring}} \dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r\, dl = \dfrac{\lambda}{2\pi \varepsilon_0}\dfrac1r \int_{\textrm{ring}}dl=$$...
3. ### Electric Potential Difference -- Conceptual Question

I am able to get V1 = kq/a - 4kq/b and V2 = kq/b + -4kq/b For some reason the solution says it is V1-V2 as opposed to V2-V1. Maybe has something to do with positive shell in the center and negative outer shell? I know the electric field goes from positive to negative, but I don't know how...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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.
8. ### 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...

10. ### 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?
11. ### Calculating the force on an electron from two positive point charges

So this is more of an intuitive question rather than a mathematical one. I present the problem. Assume I have 2 charges of charge +q at a distance r from each other on the z axis. Position of two charges is (0,0,r/2) and (0,0,-r/2). Assume now that I want to calculate the force these two...
12. ### 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...

14. ### Deriving electric and vector potential

1- Write down the complete MAXWELL equations in differential form and the material equations. 2- An infinitely extensive area is homogeneously filled with a material with a location-dependent permittivity. There are charges in the area. Give the Maxwell equations and material equations of...
15. ### 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
16. ### 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...
17. ### 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...

49. ### Confusion regarding Electric Potential Energy and Work

Hi everyone. I've been doing a lot of reading regarding electric potential and electric potential energy. Unfortunately, I have a lot of confusion regarding this topic, as I keep receiving different information. My main confusion is regarding the signs, positive or negative, of work and it's...
50. A

### External Forces and Potential Difference

Homework Statement The work done by an external force to move a -8.0 uC charge from point a to point b is 25*10^-4 Joules. If the charge was started from rest and had 5.2 * 10^-4 Joules of kinetic energy when it reached point b, what must be the potential difference between a and b? Homework...