# 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. 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...
2. A

### Accelerated Electron and its Potential Energy

Homework Statement An electron acquires 3.16*10^-16 J of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential. Homework Equations w =Δv * q The Attempt at a Solution...
3. A

### Negative work and electric potential energy

I am confused how a charge could have negative work done. To clarify, I was doing a problem earlier in which a positive charge and negative charge are moving towards each other. I used the equation work = Δv * q And when I was doing this, the change in electric potential, Δv, was negative, and...
4. A

### Finding the final speed of a Positive and Negative Charge

Homework Statement This is an example problem I found on khan academy and it didn't have an official problem statement... So I am going to have to make up my own problem statement from what was given. I can link the video if any of you want to see it. A positive charge 4uC and a negative...
5. K

### Electric field model using a cylindrical capacitor

Homework Statement In a lab experiment we measured the potential at different points within a cylindrical capacitor electric field modeling plate thing (apparently that's the best I could do to translate that into English). The positive electrode was connected in the middle and the negative...
6. I

### Connecting three spheres with wires redistributes charge

Homework Statement There are three identical conducting spheres, A, B and C. They are initially charged as q_A = 0, q_B = 0, q_C = +Q. Initially, A and B are connected by a wire. Then the spheres are connected (by a wire) as follows: 1) A to C (while A is still connected to B) 2) Connection...
7. B

### Electric Potential and Electric fields

Homework Statement Can there be a point in space where there is an electric potential but not electric field? Can there be a point in space where there is an electric field but no electric potential? Explain you answer. What would the electric field lines look like if the electric field was...
8. ### Electric potential due to a solid sphere

Hello Guys! This is my first post so bear with me. I am currently studying the basics of electrostatics using the textbook "Introduction to electrodynamics 3 edt. - David J. Griffiths". My problem comes when i try to solve problem 2.21. Find the potential V inside and outside a uniformly...
9. ### Electric potential related to electric field question

Homework Statement (i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate. (a) Find the electric field inside and outside of the sphere (b) Find and plot the electric potential inside and outside of the sphere...
10. ### Electric potential between two concentric spherical shells

Homework Statement (The complete problem statement and solution are inside the attached picture) Two isolated, concentric, conducting spherical shells have radii ##R_1=0.500 m## and ##R_2=1.00 m##, uniform charges ##q_1=2.00 mC## and ##q_2=1.00 mC##, and negligible thicknesses. What is the...
11. ### Plot 3D graph of electric potential of a charged particle

Homework Statement Plot the electric potential ##V(r)## due to a positively charged particle located at the origin of an XY plane. Homework Equations ##V=\frac 1 {4πε_0} \frac q r## The Attempt at a Solution I'm unfamiliar with 3D coordinates at this time, but I like to know how can I plot it...
12. ### Calculating work on an electron on an equipotential surface

This is not a homework, but a question formed in my mind after reading my textbook. Homework Statement Consider an electron (a charged particle) on a metallic equipotential surface. We know that all the points on the surface are equipotential, thus there will be no force on charged particles...
13. ### A problem regarding the electric potential of an electron

Homework Statement There is a sample problem in my physics textbook (Fundamentals of Physics, 10th Edition by David Halliday and others) which has some confusion in it for me. Please take a look at the snapshot I took, in the attachments. Homework Equations 3. The Attempt at a Solution [/B]...
14. ### Electric field and potential

I understand that if electric field at any point is 0, it implies that potential is constant not necessarily 0. But what if the potential at a point is 0? Does it imply that electric field is 0? Me and my friend had an argument and I am in the favour of electric field not being 0. Do I win guys...
15. ### Deriving expression for potential of a point charge

Homework Statement I am trying to derive an expression for the potential of a positive point charge by bringing in another positive test charge in from infinity to a point at a distance R from the point charge. Homework Equations $$V_f - V_i = - \int \vec E \cdot d \vec r \, dr$$ The Attempt...
16. ### Find electric potential of field inside and outside nucleus

Homework Statement Derive following expression for the electrostatic potential energy of an electron in the field of a finite nucleus of charge, ##+Ze##, and radius, ##R=r_0A^{1/3}##, where ##r_0## is a constant. (Charge density is constant.) The potential we are asked to derive is:  V(r) =...
17. ### Finding an expression for Electric Potential?

Homework Statement There is a thin rod with charge Q that has been bent into a semicircle with radius R. Find an expression for the electric potential at the center. Radius = R Charge = Q Homework Equations V = ∫(k * dq)/r The Attempt at a Solution dq = λdx λ = Q/L L = pi * r V = kQ / LR...
18. ### Calculating the Potential Energy of a 3-point charge config.

Homework Statement Charge q1= 8.5 nC is located at the coordinate system origin (0,0), while charge q2= -4.46 nC is located at (a,0), where a= 1.5 m. The point P has coordinates (a,b), where b=0.95 m. A third charge q3= 16.5 nC will b added later. It is a 3 part question, first asking for the...
19. ### How to find electric potential given only velocity

Homework Statement Given v = v=4.8×105m/s find the change in electric potential. Homework Equations ΔV = Vf-Vi = -W/q The Attempt at a Solution I really don't know any other formula that has the use of velocity to find ΔV. So how does velocity end up into the mix in finding ΔV?
20. ### Magnitude of the work done by electric field.

Homework Statement The membrane around a cell normally has layers of charge that create a potential difference between its outer and inner surfaces. This difference is about 72 mV . When a singly ionized potassium ion moves through a channel in the membrane passing from the outside to the...
21. ### Electric Potential Difference

Homework Statement Two charged rods, each with net charge -Q0 are held in place as shown in the top view diagram below. a. A small test charge -q0 travels from point X to point Y along the circular arc shown. i. Draw an arrow on the diagram at each point to show the direction of the electric...
22. ### I Probably a Dumb Question: How are E and (delta)V correlated?

What I Think I Understand: ΔV = Ed (d being dstance) and that V = kq/r please correct me if I'm misunderstanding those. What I need to know: When E = 0, what happens to the electric potential? and vice versa. Me Working it out: So if i use the first equation up here, If E = 0, then electric...
23. ### 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...
24. ### Question about work on an electric charge

Homework Statement If the electric field does positive work on a negative charge as the charge undergoes a displacement from point A to point B within an electric field, then the electric potential energy is a) negative b) positive c) increases d) decreases e) electric fields can not do work...
25. ### Help Please -- E/M conceptual question regarding electric potential

So in a graph where V is a function of x, when the slope is negative what does that mean about the direction of the field along the x axis? What about when the slope is positive?
26. ### Grounded conductor and Electric field potential question ?

Homework Statement [/B] Homework Equations V= kq/r.[/B] The Attempt at a Solution For 8-8, I do not really know how to approach it. For 8-14 , I think that q2=-q1 and q3=q1+q2. I can now use V=kq/r and then find the equations for r>R3 , r=R3 , R2<r<R3 , r=R2 and R1<r<R2 and...
27. ### Electric potential at the vertex of a triangle

I am stuck with this problem: The right triangle shown with vertex P at the origin has base b, altitude a, and uniform density of surface charge σ. Determine the potential at the vertex P. First ﬁnd the contribution of the vertical strip of width dx at x. Show that the potential at P can be...
28. ### The relation between Electric Field and Electric Potential

Homework Statement The electric field and the electric potential at a point are E and V respectively. (a) If E=0, V must be 0 (b) If V=0, E must be 0 (c) If E≠0, V cannot be 0 (d) If V≠0, E cannot be 0 Homework Equations [/B] E = V/d The Attempt at a Solution [/B] I basically substituted...
29. ### 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...
30. ### Help with determining distance where electric potential is 0

Question states 'Determine the distance from the +4.0nC charge to the point, along the straight line between the charges, where the electric potential is zero.' This is as far as I've got: so I've used V=Q/4pi(epsilon0)r and then set it so V1+V2=0 (to find the point where the resultant...
31. ### Electric Field, Potential, and Work at a Point

Homework Statement Homework Equations E = kq/r2 V = -∫ E ⋅ ds W = -Vq The Attempt at a Solution a) I just summed up the electric fields: +ek/a2 +ek/a2 -ek/a2 so I get +ek/a2 as a result. Not sure if this is correct since -e has a y component so I was thinking to use sin but not sure which...
32. ### Calculating voltage between two points....

Homework Statement Homework Equations The voltage between any two points due to the field from a point charge q is: Kirchoff's voltage laws, which states that the total voltage around a closed loop must be zero, i.e.: The Attempt at a Solution To find V(e<-d) I used Kirchoff's...
33. ### Electric Potential of a Point Charge close to R=0

Homework Statement ≈ What is a 3D representation of voltage using Kq/r assuming a positive point charge and what is the equation in cartesian and cylindrical form 2. Relavent equations Kq/r 3. Attempt at solution[/B] I was trying to get a better understanding of Voltage, to really FEEL...
34. ### Electric Potential

Homework Statement A proton is in a place where the electric potential is V, and as a result it has a potential energy E. If you replace the proton with an alpha particle (twice the charge of the proton and four times the mass) in the same place, it will experience an electric potential...
35. ### Find Electric Potential

Homework Statement A plastic circular washer is cut in half and has a charge Q spread uniformly over it. If the electrical potential at infinity is taken to be zero, what is the electric potential at the point P, the center of the old washer? The inner radius of the washer is a, the outer...
36. ### Series expansion for 2D dipole displaced from the origin

I learn that we can expand the electric potential in an infinite series of rho and cos(n*phi) when solving the Laplace equation in polar coordinates. The problem I want to consider is the expansion for the potential due to a 2D line dipole (two infinitely-long line charge separated by a small...
37. ### Methods of Images between two parallel cylinder

Homework Statement Using methods of Images, How do I find the potential of the system consisting of two conducting cylinders that are not grounded and separated at a distance of 2D, one in a potential of V_0 and the other is -V_0? Homework Equations The potential due to an infinite line...
38. ### ACTUAL Variation of Potential inside a diode.

Homework Statement The figures showing the potential variation inside a PN junction normally shows the potential to be constant in the neutral P and N regions Homework Equations V=Q/4ΠΣr The Attempt at a Solution Since the potential due to the positive and negative charges should also exist...
39. ### Capacitors in a series circuit W/ one dielectric

Problem: When a dielectric slab is inserted between the plates of one of the two identical capacitors in Fig. 25-23, do the following properties of that capacitor increase, decrease, or remain the same: (a) capacitance, (b) charge, (c) potential difference (d) How about the same properties of...
40. ### Variation of Potential outside a PN junction

Homework Statement 1. We are considering a step junction at equilibrium(no external voltage applied). 2. The potential variation is shown as negative potential at P region(which is shown as constant) and increasing through the transient region to become positive in the n region. Homework...
41. ### 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...
42. ### Potential of a spherical shell (non-uniform charge density)

Homework Statement Given a spherical shell of radius R and the surface charge density ( being the angle from the top of the sphere and being a constant) find the electric potential and the electric field inside and outside the sphere. Check that both the potential is continuous inside and...
43. ### Electric Potential due to two charges

Homework Statement Two point charges are placed on a horizontal line, the first is +3.0-μC located at x = 0.0-m, y = 0.0-m and the second is -4.0-μC located at x = 2.0-m, y = 0.0-m. At what points on the horizontal line y = 0.0 will the electric potential be zero? Homework Equations V(r)=kq/r...
44. ### Electric Potential Energy Concept

I'm unsure if the following is true or not in the absence of external forces: Electric potential is a scalar quantity. This I know is true because there is no direction associated with potential energy. It is always possible to assign a value of zero to the electric potential at the...
45. ### Electric field and potential on a singular spin helix

Hello dear physics masters on earth, I am very grateful to be priviliged to ask you a question regarding electric fields and potential of a single-cpin helix. It is portrayed as below. It is a line of uniform charge, and 1-turn helix with radius R and height H. I have came to ugly answers, and...
46. ### Electrostatics: Work required to assemble point charges

I'm studying for the physics GRE and am fairly poor with EM. 1. Homework Statement What is the work needed to assemble four point charges q into a regular tetrahedron of side length a? Homework Equations W = 1/2ΣqiV(ri) The Attempt at a Solution Assume that the origin is at one of the...
47. ### Potential of a Spherical Shell

Hi! I have trouble with solving this problem and would be really thankful for some help. :) 1. Homework Statement Inside a thin, spherical metal-shell with a radius of 50 cm, a smaller homogenous metal-sphere with a radius of 20 cm is placed concentrically. The smal sphere is grounded through...
48. ### Electric potential, Can Someone Check This?

Homework Statement A particle charge of 7.6μC is in a uniform electric field directred to the left. Another force, in addition to the electric force, acts on the particle so that when it is released from rest it moves to the right. After it has moved 8cm, the additional force has done...
49. ### I'm trying to find electric potential.

Homework Statement There is a 4 cm by 3 cm rectangle with 2.0 nC charges at three corners. I'm trying to find the electric potential of the last corner in V. Homework Equations U=(kQq)/r I think V=(kq)/r I think The Attempt at a Solution I found the U's between the know corners but i don't know...
50. ### Potential of charged cylinders

Homework Statement An infinite solid cylinder of radius A and uniform charge distribution ρ is surrounded by a thin cylindrical envelope of radius B and linear charge distribution λ. The two cylinders are co-axial. Find the potential V(r) as a function of r from r=0 to r=∞. Homework Equations...