# 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. ### 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...

40. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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...