What is Electrostatic potential: Definition and 137 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. L

    I Work to move a point charge from infinity to the centre of a charge distribution

    Electrostatic potential $$ \Phi(\vec{r})=k \int \mathrm{d}^{3} r \frac{\rho\left(\vec{r}^{\prime}\right)}{\left|\vec{r}-\vec{r}^{\prime}\right|} (i) $$ with $$ k=\frac{1}{4\pi\epsilon_{0}} $$ in SI units. What work is required to move a point charge q from infinity to the center of the through...
  2. cwill53

    Calculation of Electrostatic Potential Given a Volume Charge Density

    Part (a) was simple, after applying $$Q=\int_{\mathbb{R}^3}^{}\rho \, d^3\mathbf{r}$$ I found that the total charge of the configuration was zero. Part (b) is where the difficulties arise for me. I applied $$V(\mathbf{r})=\frac{1}{4\pi \epsilon _0}\int_{\Gamma }^{}\frac{\rho...
  3. R

    Use Gauss' Law to calculate the electrostatic potential for this cylinder

    I solved laplacian equation. and got the solution of V(r, phi) = a. +b.lnr + (summation) an r^n sin(n phi +alpha n ) + (summation) bn r ^-n sin( n phi +beta n)
  4. Ahmed1029

    I Laplace's equation in presence of a dipole (perfect or physical)

    Does Laplace's equation hold true for electrostatic potential at the location of a dipole? Or should poisson's equation be used?
  5. Ahmed1029

    I When does the second uniqueness theorem apply?

    For the second uniqueness theorem of electrostatics to apply, does the outer boundary enclosing all the conductors have to be at a constant potential?
  6. Ahmed1029

    I Exact electrostatic potential of a pure dipole using multipole expansion

    If I have a physical dipole with dipole moment p. Now, this formula for potential (V) is a good approximation when r is much larger than both r1 and r2 in the picture below. It's however said that for a pure dipole for which the separation between charges goes to zero and q goes to infinity, the...
  7. V

    B How is capacitor energy the same as electrostatic potential energy?

    The energy stored in a capacitor is derived by integrated the work needed to move charge dQ from one plate to another. I'm confused on how this energy is the same as electrostatic potential energy, the energy needed to assemble this configuration from infinity. In the case of capacitor energy...
  8. Ugnius

    Electrostatic potential and electric field of three charges

    So I started with b) and it there was no q2 this would seem reasonable I was wanted to ask , what effect does q2 have on potential of these two charges? Because it has to be given for a reason.
  9. Anonymous243

    Electrostatic potential energy of a non-uniformly charged sphere

    Hi, I'm new here, so I don't know how to write mathematical equations, and I may not be fully aware of the rules here, so I'm sorry if I made a mistake. I know how to calculate the electrostatic potential energy of a countable number of charged particles, but I don't know how to calculate the...
  10. A

    Electrodynamics: electrostatic potential

    Hi! I tried to solve it by using the equation of the electric potential above and as we see it requires the electric field, but the electric field at the center of the ring is zero. Then I tried by using the equation [text] V = \frac{1}{4\pi\epsilon_0r} \int \lamda dl [\text] and I got [text] V...
  11. Gustav

    Electrodynamics, Electrostatic potential, electric-field

    I am unsure how to solve the problem and would appreciate any suggestens on how to start solving the problem.
  12. sophiatev

    Electrostatic Potential Energy of a Sphere/Shell of Charge

    So it seems the typical way to approach this problem is to consider the sphere when it has charge q and radius r. With uniform charge density ##\rho##, this becomes ##q = 4/3 \pi r^3 \rho## and so ##dq = 4 \pi r^2 dr \rho##. Using our expression for the potential outside of the sphere, we find...
  13. C

    Electrostatic potential due to a dipole

    Given here is that by geometry r1^2 =r^2 +a^2 - 2ar*cos(theta) But if we try to do vector addition then since direction of dipole is upwards then it should be r^2 =r1^2 +a^2 + 2ar1*cos(alpha) Where alpha is the angle between a and r1. I Don,'t understand how they get it by geometry
  14. I

    Dipole moment from electrostatic potential equation

    Hello to everyone. The question or debate here is how you obtain the commonly known equation of dipole electric moment: from the electrostatic potential equation for a multipole of order n: I understand it is related with Dirac delta functions but a step by step solution might be helpful.Thank...
  15. C

    Electrostatic potential on a 3d object

    How to calculate the eletrostatic potential on a 3d object, for example a ring, if it is charger with some "Q" charge what is the potential on the surface of the ring?And how do i calculate it based on the charge of the ring?
  16. majormuss

    Finding the electrostatic potential of a square sheet.

    Homework Statement Consider a uniform surface charge density σ on a square of unit area. (a) Compute the electrostatic potential Φ along the line normal to the center of the square. My current attempt at a solution (image attached) is either incomplete or is simply wrong but I am unable to...
  17. Philip Koeck

    Potential of a solid, double cone shaped charge distribution

    Does anybody know if there is an analytical expression for the electrostatic potential produced by a charge distribution confined to a double cone shaped region. Think of a beam of charged particles converging to a focus and then diverging again. The total charge in each thin, cross-sectional...
  18. sal1234

    Electrostatic potential energy

    [Note from mentor: this was originally posted in a non-homework forum, so it does not use the homework template.] There is a general relation between the work U required to assemble a charge distribution ρ and the potential φ(r) of that distribution: U = 1/2 ∫ ρ...
  19. D

    What is the solution for the integral of 2x?

    Homework Statement Given an E field, determine if it's a possible electrostatic field. If so, determine a potential Homework Equations ∇⋅E ∇×E The Attempt at a Solution [/B] Just more of a clarification, since my friend and I both attempted this question differently. I took the...
  20. A

    How to solve this electrostatic potential integral equation with Python

    Hi! I would like solve this kind of relation: \phi = \int_0^r \phi (r') 4 \pi r'dr' But I don't know how to proceed... Can you advise me ? Thank's in advance !
  21. G

    "long-range" and "singular" electrostatic potential?

    EDIT: Problem is FIXED. Hello, I'm trying to understand Ewald Summation and finally found a great link (http://micro.stanford.edu/mediawiki/images/4/46/Ewald_notes.pdf) that I could follow in the five first pages. But then I'm blocked by a rather odd formulation p. 5, after eq. (25): "where...
  22. zonde

    I Problem with classical electrostatic potential energy

    In classical physics electrostatic potential energy is: ##U=k_e\frac{q_1q_2}{r}## So amount of potential energy is not limited as ##r\rightarrow 0## But obviously potential energy (= binding energy) is limited by masses of charge carrying particles. Say when electron and positron annihilates...
  23. Sunanda

    What is the potential of plate B with respect to infinity?

    I have two isolated plates A and B, kept parallel to each other. Now I give charge +Q to the plate A, it will redistribute itself as +Q/2 on the outer plate A and + Q/2 on the inner plate A. Right? Now this will induce charge -Q/2 on the inner plate B and +Q/2 charge on the outer plate B...
  24. F

    The electrostatic potential energy of two spheres

    Homework Statement Homework Equations The Attempt at a Solution Is my answer correct ?
  25. Sunbodi

    Distances where electrostatic potential is zero

    Homework Statement A particle carrying charge +q is placed at the center of a thick-walled conducting shell that has inner radius R and outer radius 2R and carries charge −3q. A thin-walled conducting shell of radius 5R carries charge +3q and is concentric with the thick-walled shell. Define V...
  26. Y

    Electrostatic potential of a cube with charge density

    Homework Statement Consider a uniformly charged cube with uniform charge density ρ.The ratio of electrostatic potential at the centre of the cube to that of one of the corners of the cube is? A hint on how to approach the problem's solution would be appreciated.(whether to use gauss law or not...
  27. Pushoam

    Change in electrostatic potential energy of two spheres

    We have two conducting spheres of radius r1 and r2 far away from each other. The first sphere has a charge Q. What is the change in electrostatic potential energy when they are connected together? Before the connection , Ube = ## \frac{Q^2}{8\pi\epsilon_0 r_1} ## After the connection , Uaf = ##...
  28. cheapstrike

    Electrostatic Potential Energy stored outside a shell.

    Homework Statement A point charge +Q is placed at the centre of an isolated conducting shell of radius R. Find the electrostatic potential energy stored outside the spherical shell if the shell also contains a charge +Q distributed uniformly over it. Homework Equations [/B] E=kQ/r2...
  29. lightofthemoon

    Electric Potential at Center of Sphere

    Homework Statement A solid conducting sphere of radius R and carrying charge +q is embedded in an electrically neutral nonconducting spherical shell of inner radius R and outer radius 9 R . The material of which the shell is made has a dielectric constant of 2.0. Relative to a potential of zero...
  30. lightofthemoon

    Electrostatic Potential / Work Question?

    Homework Statement An electron and a proton are held on an x axis, with the electron at x = + 1.000 m and the proton at x = - 1.000 m. If a second electron is initially at 20 m on the x axis, and given an initial velocity of 350 m/s towards the origin, it does not reach it. How close to the...
  31. oneofmany850

    Defining electrostatic potential field

    Homework Statement In a device called a betatron, charged particles in a vacuum are accelerated by the electric field E that necessarily accompanies a time-dependent magnetic field B(t). Suppose that, in cylindrical coordinates, the magnetic field throughout the betatron at time t can be...
  32. C

    Work of external forces and electrostatic potential energy

    Homework Statement Two metal spheres of equal radius ##R## are placed at big distance one from the other. Sphere 1 has total charge ##q## and sphere 2 has no charge. The two speheres are moved one towards the other until they touch, then they are moved again far away one from the other. What is...
  33. J

    What is the electrostatic potential energy of a sphere?

    Hello! I'm Steven, and I'm currently working on the following problem: The Earth can be seen as a conducting sphere with an electric field: E= -(150V/m)r (on its surface) and where r is the unit vector . The Earth has a radius 6371 km. So, I am asked to calculate the electrostatic potential...
  34. P

    Electrostatic Potential: Value at zero distance from charge

    Formula for Electrostatic Potential due to a point charge is V=1/4π∈ Q1 Q2/r This implies that at r=0 value of the potential should be infinity. Is it True. If that is the case then how we say the terminals of a battery having positive and negative charge are having definite value of...
  35. P

    Find the electrostatic potential above loop of charge Q?

    Homework Statement An electric charge Q is uniformly distributed along a thin circular wire situated in the z = 0 plane at x2 + y2 = R2 . Determine the electrostatic potential at the point (0, 0, D). Homework EquationsThe Attempt at a Solution I figured the only components that mattered would...
  36. N

    Electrostatic potential a a point, the pluses and minuses

    On calculating the electrostatic potential at a point due to charge q, by definition, it is the work done to bring a unit positive charge from infinity to that point. Trying to find it mathematically, it should be ∞→R ∫E.dr...
  37. Khaled Yasein

    Electrostatic potential of a charged disk

    How can I find the electrostatic potential of any point on a charged disk with radius R and surface charge density σ
  38. A

    Boundary conditions electrostatic potential

    I'm modelling a system with a nanosized semiconductor in 1d, inside which I want to find the electrostatic potential. Having found this I am unsure what boundary conditions to put on this, when it is connected to a metal on one side and to vacuum on the other. So far I have put that it is...
  39. J

    Solution to Laplace's equation in parabolic coordinates

    I'm stuck on a seemingly simple 2D electrostatics problem. The problem is as follows: A parabolic interface ($$x(y)=cy^2$$) separates two regions of different conductivities, with a uniform electric field at infinity aligned with the x-axis. I write the Laplace operator in parabolic...
  40. j3dwards

    Electrostatic potential inside/outside sphere

    Homework Statement A sphere of radius R carries an electric charge Q, uniformly distributed inside its volume. (a) Using the expression for the electric field given in the lectures, compute the electrostatic potential V (r) inside and outside the sphere. Homework Equations E[/B] = -∇V The...
  41. gracy

    Electrostatic potential question:what does "Slowly" indicate

    A charge s moved in an electric field of a fixed charge distribution from point A to another point B SLOWLY.The work done by external agent in doing so is 100J.What is the change in potential energy?Now that is not my actual question.I want to ask what does "SLOWLY" indicate?I know to apply the...
  42. P

    Calculating electrostatic potential energy

    Homework Statement Consider potential field V(ρ, φ, z) = V_0/ρ in free space and cylindrical coordinates. Calculate electrostatic potential energy stored in half cylindrical shell defined by a≤ρ≤b, 0≤φ≤π and 0≤z≤h. Homework Equations W_E=½∫∫∫ρ_vVdV The Attempt at a Solution I have no idea...
  43. M

    What is a potential? Specifically, an electrostatic potential

    Homework Statement How do we define an electrostatic potential? My teacher tried to explain it through teaching us gravitational potentials, and I have presented what I came up with under '3.The attempt at a solution'. Please see below and thanks in advance for any help in clarifying whether my...
  44. M

    Electrostatic Potential Energy

    Homework Statement As an electron moved through a region of space, its speed changed from an initial velocity of vi=8114.3 km/s to the final velocity vf=2233.7 km/s. The electric force was the only force acting on the electron. Across what potential difference did the electron travel...
  45. M

    Electrostatic Potential Energy

    Two charges, q1=-9.4 μC and q2=1.2 nC with masses m1=13.4 gram and m2=2.7 gram were located 8.5 cm from each other. Charge q1 is held in place. We wish to push the 2nd charge q2 as far from the 1st charge as possible. With what initial velocity should charge q2 be pushed to send it all the...
  46. G

    Electric potential at center of charged rod

    Homework Statement Find potential of a uniformly charged rod of length 2a Homework Equations -Superposition The Attempt at a Solution dV=\frac{kλdx}{r}, r=x V=λk\int\limits_{-a}^a \frac{1}{x}\mathrm dx=0 Potential at point B is zero. Is this correct?
  47. P

    Simulating Electrostatic potential

    Hello everyone, I am currently learning how to use a simulation C++ library (for those wondering, it is the deal.II library) by simulating a "simple" problem where I have a charged parallel plate in free space and I am solving for the electrostatic potential around the plates. For those that...
  48. G

    System of hollow cylindrical conductors

    Homework Statement Find potential and charge per unit length of every cylindrical hollow shell if the outer shell is grounded. The length is considered to be infinite. Homework Equations V=∫Edl The Attempt at a Solution I am not sure how to derive potentials for first two conductors...
  49. G

    Find electric potential at a center of charged rod

    Homework Statement Find electric potential at a center of charged rod with charge 'Q' and length '2a' if referent point is at infinity. Homework Equations Electric potential of a point charge: V=kQ/r Electric potential via electric field: integral (Edl) The Attempt at a Solution I used...
  50. Loonuh

    Effect of negative electrostatic potential on infinite wire?

    Homework Statement I am working on a problem that states the following: Imagine an infinite straight wire carrying a current I and uniformly charged to a negative electrostatic potential Φ I know here that the current I will set up a magnetic field around the wire that abides to the right...