# Electric potential Definition and 121 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. ### Need help in applying Binomial Aproximation when y L?

Homework Statement So I am working on an Electric Potential problem. There is a point P that is located on top of this rod ( this rod is aligned horizontally & is length L). I've solved this problem and got an answer. I want to find when y>>L using Binomial Approximation except I am quite...
2. ### Physics w/Calculus II Electric Potential, Non-Uniform Charge

Homework Statement Picture of problem is attached A rod of length L lies along the positive y-axis from 0<=y<=L, with L = 0.400 m. It has a positive nonuniform linear charge density (charge per unit length) λ = cy2, where c is a positive constant and has a numerical value of 8.00 x 10-7. (a)...
3. ### Can Electric Potential Be Understood On Intuitive Level?

There are two situations with electric potential that confuse me. They're the spots midway between two point charges. If the charges are the same, then the electric field is zero and a test charge would not move if placed there. How can there then be electric potential in that spot? If...
4. ### Determine The Speed of a Charge at a given point

Homework Statement Given: The electric potential function: V= 3x^2 + 2xy +(y^2)z + 20 a) A 4 coulombs, 2kg charge is released from the origin. Determine the speed of the charge at (1,1,-1) Homework Equations Kinetic Energy= 1/2 mv^2 The Attempt at a Solution I tried to use the fact that the...
5. ### Where between two charges does voltage = 0?

Homework Statement If Q1 in the above figure is twice Q2 and both are positive, where can a point of zero potential be found? Homework Equations V = kq/r The Attempt at a Solution I know that eventually I'll have to set it up so that kq/r = kq/r, but my problem is, how do you know where...
6. ### Superposition principle for potential?

Homework Statement A solid, conducting sphere of radius "a" and charge -Q is concentric with a spherical conducting shell of inner radius "b" and outer radius "c". The net charge on the shell is +3Q. Take the zero of electric potential to be at some point at infinity. a.) Use Gauss's law to...
7. ### Potential difference between wire and ground

Homework Statement A long, straight power line is made from a wire with radius ra = 1.0 cm and carries a line charge density λ = 2.6 μC/m. Assuming there are no other charges present, calculate the potential difference between the surface of the wire and the ground, a distance of rb = 22 m...
8. ### Pointlike charge - electric potential

This is my first time using a website like this, so I sincerely apologize if I'm posting in the wrong spot, I'm just in a bind/frustrated with this seemingly easy problem. Homework Statement What is the electric potential at a point 0.80 m away from a point charge of 3.5m C? Homework...
9. ### Electric potential of a cube of 8 point charges

Homework Statement Find the Electrostatic potential energy of a cubical configuration of point charges. (One charge on each corner of a cube). Each of the charges is 3.00e and the edge of the cube is 3 cm. Homework Equations U = kqQ/r The Attempt at a Solution I'm pretty sure I understand...
10. ### Two charged nonconducting sphere shells

Homework Statement One of two nonconducting spherical shells of radius a carries a charge Q uniformly distributed over its surface, the other a charge -Q, also uniformly distributed. The spheres are brought together until they touch. What does the electric field look like, both outside and...
11. ### Total electric potential energy of equilateral triangle

Three charged objects, (+4 micro coulomb, -4 micro coulomb and +2 micro coulomb) are placed at the corners of an equilateral triangle with side length 2m. Calculate the total electric potential energy of the system... Guys Can you help me achieve a solution to this question? Thanks In Advance!
12. ### Conceptual Question about electric potential

Guys, i really need help on answering this question... Can a charged particle ever move from a low electric potential to a high electric potential and yet have its electric potential energy decrease? Explain. What i think is that, no it is not possible for a charged particle to move to a...
13. ### Zero Electric Potential Concept and Visualization

Homework Statement Hi, I've been having problems visualizing and interpreting a situation where there is zero potential in a point, equidistant, between two opposite charges. What is the significance of this? Here's a sample problem: Consider two point charges. One has a charge of +1 μC and...
14. ### Electric potential ( with angle)

Homework Statement The electric potential of a region of space is V= 200 / sq root (x^2 + y^2), where x and y are in meters. What are the strength and direction of the electric field at (x,y) = (2m,1m)? Homework Equations The Attempt at a Solution I took the negative derivative of V to...
15. ### Electron move through capacitor

Homework Statement An electron enters a region between two capacitor plates with equal and opposite charges. The plates are L=0.1 m by d=0.05 m, and the gap between the plates is h=0.002 m. During a short time interval of dt=0.002 s, while between the plates and far from the edges, the change...
16. ### Electric Field due to Point Charges

Homework Statement [/B] The following is on a practice exam I have been completing. In advance, it is part b I am struggling with. Two point charges Q1 = +5*10^(-6)C and -2*10^(-6)C are 50cm apart. a) Where along a line that passes through the two charges is the electric potential zero (apart...
17. ### Determining Electric Potential

Homework Statement Consider a nonconducting sphere of radius r2. It has a concentric spherical cavity of r1. The material between r1 and r2 has a charge density p (C/m3). Take V=0 and r=infinity. Determine the electrical potential V as a function of the distance r from the center for (a) r>r2...
18. ### Electric potential linear charge

Homework Statement A charge Q is uniformly distributed along a straight line of length a. Calculate V by integration, choosing the origin of the coordinates as the center of the charge. Next, expand this value of V up to terms in 1/r^2 Homework Equations V = \frac{\lambda}{4 \pi \epsilon_0 r}...
19. ### Finding the acceleration of an ion across a potential difference of a given thickness

Question Assuming the electric potential difference between the inside and outside of a cell is 70 mV and the thickness of the region across which this exists is 7 nm, calculate the acceleration a chlorine ion would experience in the absence of other forces. In the absence of other forces how...
20. ### Find the potential difference in a rectangle

Homework Statement [/B] Figure 20-3, referred to below, is 0.800m wide and 0.400m tall with "A" in the top left corner, "+4 microC" charge in the top right corner, "+2 microC" charge in the bottom left corner, and "B" in the bottom right corner. Two point charges of magnitude +4.00 μC and...
21. ### Conductor with shell problem getting zero as answer?

1. Problem Statement: The figure shows a cross-section view of a very long cylindrical cable. There is an outer tube made of copper, inner radius 2R, outer radius 4R. The inner copper wire has radius R and is concentric with the tube. The inner wire has charge density –2λ (per unit length)...