# What is Electric potential energy: Definition and 182 Discussions

Electric potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects.
The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields.

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1. ### Minimizing the Energy of Two Conductors Very Far Apart

The work done by the electric field when we bring a charge ##dq## from an infinite distance to the surface of a shell with radius ##r## is $$dW=\int_{\infty}^r \frac{Qdq}{4\pi\epsilon_0 r^2}dr=-\frac{Qdq}{4\pi\epsilon_0r}\tag{1}$$ The work done by the electric field to charge a spherical shell...
2. ### Several questions relating to work, electric potential energy, and potential difference

I have several questions relating to electrostatics: first of all, in this derivation for the formula of the electric potential energy: work is being done against the electric field right, so the work should be negative, but in this case it's positive. I'm wondering if it's because the direction...
3. ### 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.
4. ### 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...
5. ### 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...
6. ### 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...
7. ### Understanding Electrical Potential Energy of a charge distribution

I quite understand the fact the EPE (Electrical Potential Energy) of a system of two charges are U = k*qQ/r, Q is fix. however when it comes to three charges i get lost. because my reasoning is : if q1 is fix then the EPE of the system when q2 is brought is U2 = k*q1*q2/r12, when q3 is brought...
8. ### Is the 'test charge' in electric potential energy defined as immobile?

Hello, quick question, when EPE was defined, did we decide that the "test charge" is immobile in the field? Otherwise a force equal and opposite to that of the electric field would just stop the charge from accelerating.
9. ### Comparing 100J and -100J of Electric Potential Energy

Is the 100 J of electric potential energy actually greater than -100 J of electric potential energy?
10. ### 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...
11. ### Are the answer choices wrong? (electric potential energy)

Homework Statement Homework Equations U=kq1q2/r The Attempt at a Solution W = changeU = Uf-Uo Uf = k(7*(-5) + 7(-4) + (-5)*(-4))/0.1 = -4.3*10^-4 Ui= k((7*(-4))/0.1= -2.8*10^-4 Uf-Ui = -1.5*10^-4k J
12. ### Electric potential energy between charge and moving magnet

The setup for one magnet Introduce a magnet: Inertial Frame 1 (or lab frame) A frame where a magnet is seen to move with uniform velocity v and carries a uniform polarization P while a point charge Q is seen to be stationary at time t=0. Inertial Frame 2 (or material frame) A frame where a...
13. ### Understand Electric Potential Energy, Difference & Potential

Homework Statement My textbook is no help, my teacher is no help, so I've found myself here. I am having a difficult time understanding the differences in 1.Electric Potential energy 2. Potential Difference 3. Electric potential Im sure this question has been asked tons of times but I need...
14. ### Find the electric potential energy

Homework Statement Homework Equations ##V= \frac {kq}{r}## ##V= \frac {U}{q}## The Attempt at a Solution ##V= \frac {kq}{r}## = 9*109*-5*10-9 /0.1= -450 V ##U= \frac {V}{q}## = -450 * -2*10-9 = 900nJ Is my answer correct ?
15. ### Finding initial velocity of two elementary particles

<Moderator's note: Moved from a technical forum and thus no template.> I'm not sure how they got the extra (1/2)mv^2? My question is shown using pink font in the image below as well as my attempt.
16. ### Change in electric potential energy

Homework Statement As an electron (q2) moves from point A to point B, it moves farther from a positive charge (q1). Does the electric potential energy increase, decrease, or stay the same. Homework Equations U=-kq1q2/r The Attempt at a Solution The electric potential energy decreases in...
17. ### When Electric Field is 0 is potential also 0?

So here is how my book defined electric potential. If you take a charge, it will have a corresponding electric field associated with it. If you put another charge in that electric field, an electrostatic force will act on it and give it kinetic energy. This kinetic energy can't come from thin...
18. ### Electric Potential vs Electric Potential Energy

So in my physics textbook a problem is stated. We are given an external electric field directed downwards of 150N/C. We are then told that an electron is released in the electric field and it moves upwards 520m. Finally we are asked to calculate the change in electric potential energy of the...
19. ### Confusion regarding Electric Potential Energy and Work

Hi everyone. I've been doing a lot of reading regarding electric potential and electric potential energy. Unfortunately, I have a lot of confusion regarding this topic, as I keep receiving different information. My main confusion is regarding the signs, positive or negative, of work and it's...
20. ### How do you calculate Electric Potential Energy in a Square?

Four identical particles, each having charge q and mass m, are accelerated from rest at the vertices of a square of side L. How fast is each particle moving when their distance from the center of the square doubles? I used the Conservation of Energy => Kf= -deltaU = Ui-Uf 4(mv^2 /2) = kq^2...
21. ### Conservation of electrical energy on a conductor

I'm having trouble seeing how electric potential energy production on a conductor follows conservation of energy. Let's use the photoelectric effect as an example. A photon with energy E = hν strikes a conductor, ejecting a photoelectron with a maximum kinetic energy of hν - φ. Assuming the...
22. 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...
23. 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...
24. 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...
25. G

### Electric Potential Energy - Final Velocity

Homework Statement Four protons (each with mass 1.7 10-27 kg and charge 1.6 10-19 C) are initially held at the corners of a square that is 7.1 10-9 m on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the...
26. ### 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]...
27. ### 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...
28. ### Find change in electric potential energy

Homework Statement A uniform electric field of magnitude 4.1 ✕ 10^5 N/C points in the positive x-direction. Find the change in electric potential energy of a +5.3 µC charge as it moves from the origin to each of the points given below. (a) (0, 6.9 m) __ J (b) (6.9 m, 0) __J (c) (6.9 m...
29. ### Radius of Half Electric Potential Energy

Homework Statement There is a solid cylinder of radius a and then empty space then a shell cylinder of radius b. Show that half of the stored potential energy lies within a cylinder of radius $$\sqrt{ab}$$ Homework Equations In the attempt The Attempt at a Solution I'm not sure what they...
30. ### Electric Potential Difference during thunder storm

Homework Statement During a thunder storm, movement of water molecules within clouds creates friction which causes the bottom of the clouds to become negatively charged. This means that the bottom of the cloud and the ground begin to act like parallel plates. Once the electric field between the...
31. ### Help with understanding electric potential graphs

Please could someone explain to me the graph on the left (for the positive source charge). I understand that the value for electric potential will be positive because of the source charge being positive, but why does it appear to decrease to zero at infinity, when the graph on the left (for the...
32. ### Electric Potential Energy Problem. Intuition needed

There's this problem that was given in my physics class.. "Three identical, negatively charged particles are situated at rest in a straight line, as shown below. All three are released simultaneously, and are free to move. Find the maximum velocities attained by particles A, B, and C. They have...
33. ### Electric Potential Energy

I am confused about the signs in calculating the potential energy change from the electrostatic force. Suppose there was a point charge +q1 and I moved a second point charge +q2 from a distance of b from q1 to a distance of c from q1. c is smaller than b. So the potential energy change is - ∫...
34. ### What is the potential energy of this group of charges?

Homework Statement Three electrons form an equilateral triangle 0.800 nm on each side. A proton is at the center of the triangle. Homework Equations U = k[(q_1*q_2)/r] The Attempt at a Solution I tried to use the following equation: k*[(3e^2)/(0.8*10^-9) - (3e^2)/(0.4*10^-9)] I plugged in...
35. ### Total electric potential energy

Homework Statement My textbook states that for point charges ##q_1, q_2, ... ,## where distance between ##q_i## and ##q_j## is ##r_{ij},## the total potential energy U is the sum ## U = \dfrac{1}{4\pi\epsilon_0} \sum_{i<j} \dfrac{q_iq_j}{r_{ij}} ## and specifically mentions not to count them...
36. ### Conservation of electric potential energy

Homework Statement An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 3.6×10−3c, where c is the...
37. ### Electric potential energy and work

Homework Statement Positive point charge (Q = 8 μC, mass m = 19 g) is fixed at point (9 cm,0). A second identical charge q is constrained to slide on a frictionless wire along the y-axis. Assume: the only force on q is the electrostatic force. If q starts at (0,7 cm) and is released from...
38. ### Potential Gradient [Question(s) regarding the concept]

[Note from mentor: This was originally posted in a non-homework forum so it doesn't have the homework template.] ----------------------------------------- Problem: The surface of a solid metal sphere (radius r = 4.58 cm) is at potential V = 9,851 Volts. Find the magnitude of the potential...
39. ### Why it's (1/2)? [Electric Potential Energy]

My question is, why it's 1/2 [qiVi]? Shouldn't it just be qiVi? Thank you ...
40. ### Isn't Born-Landé equation double the electrostatic energy?

I'm confused as to how the Born-Landé equation can be extrapolated to find the electrostatic potential for an ionic lattice without halving it, as each interaction is otherwise counted twice. As I understand it, and according to Wikipedia, the electric potential energy in a charge configuration...
41. ### Electric potential Energy

Homework Statement Describe the motion of a test charge in a non-uniform electric field.By considering the electric forces acting and Newton’s second law, explain the type of motion occurring in a non-uniform electric field. Homework EquationsThe Attempt at a Solution I wrote that the...
42. ### Electric Potential and Kinetic Energy

Homework Statement A charged particle (q = -8.0 mC), which moves in a region where the only force acting on the particle is an electric force, is released from rest at point A. At point B the kinetic energy of the particle is equal to 4.8 J. What is the electric potential difference...
43. ### Voltage drop and potential energy

Hi! What is the potential energy of electrons converted to, in a circuit? I'm asking this question because I don't really understand the concept of voltage drop across some element. If I have a series circuit with a 10V battery and two equal-in-magnitude resistors, then the potential...
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. ### Why use conservation of energy in particle velocity problems

Suppose we have an electric field, and push a proton or electron through it (from rest). We're accelerating it through an electric potential difference of some kind. Why do we apply conservation of energy to the particle-field system to find the speed of the particle? Example: Calculate the...
46. ### Electric Potential Energy Inside a Charged Sphere

Homework Statement A point charge q<0 lies just outside a uniformly and positively (non-conducting) charged ball. Assume the charge can pass through the ball freely. Describe the motion of the charge. Homework Equations Coulomb's force law, energy equation. The Attempt at a Solution Obviously...
47. ### Electric Potential Energy & Electric Potential

Two frictionless pucks are placed on a level surface, as shown, at an initial distance of 20 m. The mass of puck 1 is 0.80 kg and it has a charge of +3.0 x 10^-4 C, while puck 2 is 0.40 kg with a charge of +3.0 x 10^-4 C. The initial velocity of puck 1 is 12 m/s [E] and the initial velocity of...
48. ### Sign on change in electric potential energy

Homework Statement I'm trying to figure out why potential energy decreases in this situation http://imgur.com/9PfjRVE [Broken] Homework Equations ΔU = FΔy The Attempt at a Solution If I define up to be positive, and ΔU = FΔy. In this picture, force is pointing down (so it is negative) and the...
49. ### Electric Potential Energy Conversion

Hello everyone, Imagine two points that have a Electric Potential Difference of 10V and they are connected through a conductor wire. Let's call these points A and B: Now imagine we have a charge on A of 1C. To move the charge to B, we need to make a work of 10J, right? So, now, imagine the...
50. ### Electric Potential Energy and Sign

There is a negative point charge with a positively charged plate above it and a negatively charged plate below it. Define up as positive and down as negative. When the point charge moves towards the positively charged plate it does negative work. Why? The force the charge experiences is upward...