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. C

    Potential and Electric Field near a Charged CD Disk

    Hi! I am a very lost physics student here. I got a) but I have no idea how. The formula I used was from an online source and it was: I think I need a contextual explanation of this formula before I attempt b). My understanding of electric potential is that it is NOT potential energy, but...
  2. C

    Semi-circular charged rods

    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...
  3. Z

    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...
  4. P

    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...
  5. yucheng

    I Electric potential and potential difference

    Electric potential = "absolute potential" Textbooks usually connect both ends of two capacitors, of different voltages, in parallel. What would happen if we only connect one end of the capacitors? Perhaps we would have to solve for Maxwell's coefficients of potential for these two cases (to...
  6. Z

    MIT OCW, 8.02 Electromagnetism: Potential for an Electric Dipole

    Here is a depiction of the problem a) The potential at any point P due to a charge q is given by ##\frac{kq}{r}=\frac{kq}{\lvert \vec{r}_s-\vec{r}_P \rvert}##, where ##r## is the distance from the charge to point P, which is the length of the vector difference between ##\vec{r}_s##, the...
  7. Jake357

    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.
  8. Jake357

    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.
  9. sinus

    I Grounded Means Zero Electric Potential: Exploring the Method of Images

    Can anyone explain to me why grounded means zero electric potential. I confuse what's the relation between infinite ground conducting plane and its electric potential (the method of images). I have a several question: 1. Why the conductor plane must be infinite, while in reality there's no...
  10. C

    Calculating Electric Potential for a Non-Negligible Thickness Toroid

    For A.1 of this problem, The solution is However, I have a doubt about the linear charge density ##\lambda##. I don't understand how ##\lambda = \frac {q}{2\pi R} ## since this is not a thin ring, but has a non-negligible width of ##2a## I think that the toroid has a larger area than thin...
  11. C

    Graphing electric potential for two positive charges

    For part (a) of this problem, The solution is However, my solution is Am I correct? In the solutions that don't appear to plot the electric potential as units of ## \frac {k_eQ} {a} ## like I have which the problem statement said to do. Many thanks!
  12. C

    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.
  13. T

    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...
  14. N

    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...
  15. MatinSAR

    Problem about electric potential

    Can anyone help me how to solve this problem ?! I am sure that my answer is not right :
  16. J

    Velocity of two masses due to electric potential energy

    We can find the potential energy by finding the potential difference between the two masses. the minimum distance between the two masses is 10 cm. The maximum is 30 cm because they can be 3 string lengths apart as they repulse each other once the string is cut. So, to get potential difference...
  17. G

    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, $$V_Z=\int_{\textrm{ring}} \dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r\, dl = \dfrac{\lambda}{2\pi \varepsilon_0}\dfrac1r \int_{\textrm{ring}}dl=$$...
  18. A

    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...
  19. L

    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...
  20. iochoa2016

    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...
  21. V

    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...
  22. bluesteels

    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.
  23. guyvsdcsniper

    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...
  24. F

    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...
  25. jaumzaum

    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...
  26. yucheng

    What's wrong? Electric potential of a point on a ring

    So I have a ring(red) of uniform charge ##\lambda## per unit length, and I want to calculate the electric potential at the origin (actually on any point of the ring). It is clear that the ring is given by the equation $$r=2 R \sin \theta$$, in polar coordinates, where R is the radius of the...
  27. E

    I Co-rotating electric potential for KN solution

    I am trying to work out the co-rotating electric potential ##\Phi = \xi^{\mu} A_{\mu}## for the KN solution. First it's necessary to prove that the hypersurfaces ##r = r_{\pm}## are Killing horizons ##\mathcal{N}_{\pm}## of a Killing field of the form ##\xi = k + \Omega_H m## for some Killing...
  28. RodolfoM

    Electric potential inside a hollow sphere with non-uniform charge

    I tried to find the charge distribution using the given potential but couldn't produce the correct result. Also, Gauss's Law doesn't help, as the electric flux is 0 but we don't have any symmetry. Can someone please shine a light on this? Thanks in advance..
  29. J

    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?
  30. A

    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...
  31. Z

    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...
  32. D

    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...
  33. A

    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
  34. greg_rack

    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...
  35. greg_rack

    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...
  36. greg_rack

    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...
  37. Athenian

    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...
  38. Sj4600

    Electric Potential Energy Question: Electron and Proton accelerating between charged plates

    Ve=0m/s Vp= 0m/s Qe/Qp= 1.60E-19 Me=9.11E-31 Mp-1.67E-27 Ive pretty much gathered all of the equations I think I need to solve the problem. I just am stuck. The last step I realize that the forces would be equal to each other so I have mp x ap = me x ae but then when I try to solve for the...
  39. B

    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...
  40. D

    Voltage using different references

    The problem is for a solid sphere uniformly charged with Q and radii R. First I calculated taked ##V(\infty)=0##, giving me for : $$ \begin{align*} V(r)=&\frac{3Q}{8\pi\varepsilon_0 R}-\frac{Q}{8\pi\varepsilon_0 R^3}r^2\qquad\text{if $r<R$}\\ V(r)=&\frac{Q}{4\pi\varepsilon_0 r}\quad\text{if...
  41. Kaushik

    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...
  42. F

    Charge rearrangement on conducting spheres

    Hi, I think this problem is solved in exactly as a similar problem where the two spheres are very far apart and connected by a very long thin conducting wire. I'm trying to explain this in words, since LaTeX does not seem to work any more (for some reason LaTeX syntax is not replaced by maths in...
  43. hairey94

    What are the assumptions for solving the charged conducting disk problem?

    Not sure how the problem set up initially as no diagram was provided in the question. Please help me to start with the solution. Your assumptions and educated guess are appreciated.
  44. mcastillo356

    Increasing electric potential and electric field

    Hello everybody! I want to check out if I've solved correctly: ##\Delta{V}=-E\Delta{x}## ##\dfrac{\Delta{V}}{\Delta{x}}=-E## ##\dfrac{15\;V}{10^{-2}\;m}=-E## ##1,5\times{10^3}\;N/C=-E## ##\vec{E}## direction it's oriented into the XY plane Thanks!
  45. G

    Electric field and electric potential exercise

    a) \vec{F}=\vec{E}\cdot q \phi =\oint \vec{E}d\vec{S}=\oint \vec{E}d\vec{S}=\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \perp}+\underbrace{\oint \vec{E}d\vec{S}}_{\textrm{FACES } \parallel}=0+\oint EdS\cdot \underbrace{\cos 0}_1= E2S \dfrac{Q_{enc}}{\varepsilon_0}=\phi \left...
  46. E

    Ambiguity when taking the Earth as a zero for electric potential

    When you ground something in electrostatics, the potential of that body becomes the potential of the Earth once equilibrium has been reached. In this context, it is usually taken that the Earth is at 0V. There are two possibilities for this. Either the constant of integration is chosen such that...
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