# What is Electrical potential: Definition and 113 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.

View More On Wikipedia.org
1. ### Confusing definition of electrical potential energy

If the book had said that electrical potential energy is the negative of work done by electrical force on a charge, then the definition would be very clear and easy to understand. So, why should the book give this confusing definition instead.
2. F

### Kinetic and potential energy of a particle attracted by charged sphere

Hello, I have a particle at point A with charge ##q_A##, and an unmovable sphere of radius ##R_B## at point B with a volumic charge density ##\rho##. The distance from particle A to the centre of the sphere in B is ##r##. Both objects have opposed charges, so, the particle in A, initially at...
3. ### Mass difference due to electrical potential energy

I do not really know the relationship between potential energy and mass difference. Isn't the difference in mass of protons and neutrons due to their quarks? (the neutron is made of two down quarks and an up quark and the proton of two up quarks and a down quark.) Please help.
4. ### Solving for Electrical Potential Energy: Durcell's Example

This question is an example in Durcell's Electricity and Magnetism. The solution goes as follows: [In this case] there are four different types of pairs. One type involves the center charge, while the other three involve the various edges and diagonals of the cube. Summing over all pairs yields...
5. ### 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...
6. ### Energy, current and electrical potential of a particle accelerator 🎆

Hello, I have answered the question below but would like some advice on whether I can improve my answer or if anyone is able to check whether I have made any mistakes ? i. 1 V = 1eV in a 1:1 relationship, therefore; 6.5 TeV = 6.5 TV = 6.5 *10^12V ii. E=W W=V * Q Q=number of particles * charge...
7. ### Electrical potential energy questions for a battery circuit

I’m trying to learn about simple circuits but I have a few questions because I don’t fully understand what’s going on . 1. If the reason current flows when a wire is connected to the ends of a battery is due to a potential difference across a battery , why can’t the current just flow through...
8. ### Determine the Electrical potential at a given point

A rod with a circular center in the middle (which causes the rod to change direction by 90 °) has an evenly distributed linear charge density 𝜆 of electrons along the entire rod. Determine the electrical potential of the red dot in the figure below which is at the center of the circular round...
9. ### Schrodinger's Equation in terms of vacuum permittivity?

Summary:: How can Schrodinger's Equation be written relative to vacuum permittivity I am wondering why a particular problem uses this equation: It is stated to be Schrodinger's equation. Where does the potential come in, as well as the e^2/r ? An explanation would be greatly appreciated. Thanks.
10. ### Electrical potential of a thin wire in an E field

Assume that an infinite metallic plate A lies in the xy-plane, and another infinite metallic plate B is parallel to A and at height z = h. The potential of plate A is 0, and the potential of plate B is constant and equal to V. So, there is a uniform electrostatic field E between plates A and B...
11. ### Electric Potential on the axis of a truncated cone

1.Data: We have an truncated cone with a volumentric charge density ρ, and it's uniform. The image show the truncated cone and show some info of the radios. 2. Question. We need to calculate the potential on the vertical axis. note: adding an image of the problem but it's in spanish, hope...
12. ### What happens to the Electrical Potential the closer we are to a point charge?

So I have been wondering: The potential for a point charge at the origin, is described as: (Using the reference point at infinity): V=1/(4πε) * q/r My question is, what happens to this Potential the closer we are to the point charge, and so the closer we would get, the Potential seems to go...
13. ### Electric Potential Distribution in a Vacuum Diode

Homework Statement This problem is belonging to a book, which is material for Vietnamese students who will take part in IPhO (International Physics Olympiad). Since this problem is written in Vietnamese, I will try my best to translate it to English: A vacuum diode consists of two parallel...
14. ### Electrical Potential and an Integration path

I have been looking everywhere for a clear explanation for the following: How do I know which way to integrate the electrical field, when I'm looking for the potential between to points? Example: I have to find the potential between the top conducting plate and the bottom conducting plate...
15. ### Electrical Potential of a uniformly charged spherical shell

Homework Statement From Griffiths Third Edition: "Introduction to Electrodynamics" p.p. 81 ex. 2.6 "Find the potential inside and outside a spherical shell of radius R, which carries a uniform surface charge. Set the reference point at infinity. Homework Equations V(r) = -∫E⋅dl The...
16. ### Analogy for Electrical potential

When the eletctric field was defined I could totally relate to E is like g in mechanics. But for the electric potential I don't know. What would be equivalent analogy?
17. ### Extrema of electrical potential

Homework Statement A charge of 2 C is located at the origin. Two charges of −1 C each are located at the points (1, 1, 0) and (−1, 1, 0). If the potential φ is taken to be zero at infinity (as usual), then it is easy to see that φ is also zero at the point (0, 1, 0). It follows that somewhere...
18. ### Uniform Electrical potential energy

Can someone explain the math of how potential energy travels from higher potential energy to lower potential energy (PE) along a uniform electric field? I understand that in order for the point charge to move, gaining kinetic energy, it will lose potential energy. But using the equation...
19. ### Does a rotating conductor generate a voltage change

Does a rotating conductor generate an electrical potential due to charges "feeling" a centrifugal force?
20. A

### Electrical Potential Energy and Potential

Homework Statement An electron that accelerates from a point near a collection of negative source charges toward a point near a collection of positive source charges experiences A) a decrease in electric potential energy as it moves toward a region at a lower electric potential B) a decrease...
21. ### Calculate electric potential from a graph

Homework Statement A region of space has a non-uniform electric field that points in the +x-direction and has magnitude as shown in the figure (Figure 1) As a reference point, take the potential at the origin to be -140 V . Calculate the electric potential at x=3.0m. Express your answer to two...
22. ### Stuck on an Electrical Potential Energy Question

Homework Statement A charge of Q = −1 µC is moved from point A to point B. Which of the following situations will result in an increase in electrical potential energy? I've now uploaded the files below Homework Equations F = qE U = qV a b c d e f g h The Attempt at a Solution I think...
23. ### How can an object move without acceleration?

hi every one. ive been digging around on the idea of volt edge and have come across the idea that potential difference is the difference in electrical potential. this is the energy required to move a particle between two reference points without acceleration? i apologies at my lack of knowledge...
24. ### Electrical Potential Energy and Electric Potential

Hi. Getting straight to the point, what is the difference between electrical potential energy and electric potential? Please be as specific as you can. Thank you.
25. ### What is the electrical potential at point P?

Homework Statement Three point charges of +6.00 μC, +4.00 [/B]μC, and +6.00 μC are placed along the x-axis 0.200 m above the +4.00 μC charge as shown in the figure below. What is the electrical potential at point P (relative to infinity) due to these charges? Diagram...
26. ### Irrelevance of electrical potential

In regards to voltage and electrical potential, I have a question. I understand the voltage to be the difference in electrical potential of two separate points. So in an analogy am I correct to compare this to a bowling ball being 4 feet off the ground. So the bowling ball has a gravitational...
27. ### Exploring Electrical Potential Energy Across Series Circuits

Assuming the resistance of a wire in a series circuit, consisting only of 1 component (e.g. filament lamp) and a battery, is negligible; does each Coulomb of charge commit all of its electrical potential energy, supplied by the battery's potential difference, as work done across the component...
28. ### Question about electrical potential energy

Homework Statement Two charged plate hold a charge of 3 coulombs with the upper plate being positively charged and the lower plate being negatively charged. They have a pd of 6 volts. There is a spacing of 20 cm between them. A positive charge q with a charge 0.4 coulomb is located at midpoint...
29. ### Calculating Total Energy of an Electron Orbiting a Hydrogen Nucleus

Homework Statement Prove that the total energy of an electron orbiting a hydrogen nucleus is Etotal = -e^2/ 8ε0 π r where e is the magnitude of charge of an electron and r is the orbital radius. Homework Equations Knowledge The Attempt at a Solution Here is my attempt: For KE, mv^2/r =...
30. ### Electrical potential energy question

Why does the potential energy of a system of two charged particles decrease as the distance between them increases? It seems that the PE should increase, as in U=mgh; as h increases, the PE increases. Why does this not occur in electrical potential energy, and in the gravitational potential...
31. ### Electrical potential of a conducting spherical shell

Homework Statement Hi everybody! I would like to clear up some doubts I have about my electromagnetism homework: A positive point charge ##q## is placed in the center of an ideal conducting electrically neutral spherical shell, as shown in the attached picture. a) Calculate the electrical...
32. ### Show that the equipotential lines are circles

Homework Statement In a specific area of the space, an electrical potential is given as: $$V(x,y,z) = A(2x^2 - 3y^2 - 3z^2)$$ where A is a constant. a.) Determine the electrical field E for any given point in the area. A test charge q_0 is moved from the point...
33. ### Electrical potential of the sphere

Metal ball ( Figure 5) radius a = 5 cm , is surrounded by two concentric metal shell of radius b = 10 cm and c = 15 cm , and d = 20 cm and e = 25 cm . The relative permeability of the dielectric between the ball and the first shell , and between the two shells is εr is 4. Outside the outer cross...
34. ### Questions based on derivation of electrical potential energy

Consider a system of two charges ## q_1## and ##q_2## separated by distance ##r_1##.This configuration is associated with a potential energy ##U_1##.When the separation is increased to ##r_2##.Potential energy becomes ##U_2## ##dW_E##=##\vec{F}##.##\vec{dr}##...
35. ### Graviational vs Electrical Potential

Hi all, Thanks for taking your time to help me. It means a lot! For some context: I'm a physics student taking an analytical chemistry course and am a bit confused by the concept of electrical potential. Gravitational potential is the potential energy per unit mass, V(gravitational) = U/m. (I...
36. ### Electrical Potential Energy of three quark system

Homework Statement A proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 3×10-15 m and calculate the potential energy of the subsystem of...
37. ### Why does the same current flow through resistors in series?

This is something I have been trying to figure out lately, but I can't seem to wrap my head around it. So, according to a definition in my Physics textbook, while the electrical potential difference established between two terminals encourages the movement of charge, it is resistance that...
38. ### Two charges, Electrical Potential

Homework Statement Two charges q = 9.0μ C are fixed in space a distance d = 1.5 cm apart, as shown in the figure. a) With V = 0 at infinity, what is the electric potential at point C? b) You bring a third charge q = 9.0μC from infinity to C. How much work must you do? c) What is the...
39. ### Electrical Potential between 2 points

Mentor note: Member warned about posting a question without the template 1. Find the electrical potential between A and B given that R1=R2=R4=100 Ohms; Power dissipated by R3 is 200 mW at 9 Volts [ code ] A---------R1-----------*------------------- | |...
40. ### Charging an earthed conductor?

Homework Statement I never quite understood the principles of earthing, but I think that the general idea is that if you have an object with excess charge (whether positive or negative), then connecting it to the Earth with a conductor will mean that either the excess electrons flow to the...
41. ### Electrical potential involving a spacecraft

Homework Statement Been stuck on this problem. Any help will be greatly appreciated 1. The (actual) spacecraft Deep Space 1 tested an ion drive engine in which Xenon atoms were accelerated (maximum voltage of 1,300 volts), neutralized and used to provide thrust. The probe carried 74 kg of...
42. ### What is the relationship between electric potential and electric field?

Q1: Use the graph (see attachment) to write the empirical equation V(r) for a charge cylindrical shell with appropriate constants, including units. Show all work. Q2: What is the interpretation of the horizontal axis intercept? Q3: What is the significance of the slope of the graph? I...
43. ### Electrical potential inside a sphere using integration

Homework Statement Find the electrical potential inside a spherical shell carrying a total charge Q by integrating over the surface.Homework Equations E=k q/r^2The Attempt at a Solution I know the answer is zero from Gauss's law, but I don't know how to do the integration to get it.
44. ### Electrical potential and potential difference

Indian school books say -- We define the electrical p.d. between two points in an electrical circuit carrying some current as the work done to move a unit charge from one point to other! =>V=W/Q But, my doubt is...since work done is directly proportional to distance between two points...
45. ### How Is Electrical Potential Derived from a Ring Charge?

Hi. I have no idea how to do this. It's complicated because the length here is a variable. I posted the same question before but there was a little mistake so I am reposting this again. The picture below shows the potential due to ring charge. Please show the full steps of deriving the...
46. ### How High Can Electrical Potential Get Near Large Charges?

The problem is to find the potential at a point that is 3 meters away from two charges. (one 3 meters above, and the other 3 meters below) q1=3μC q2=6μC I put that Ep=Epq1+Epq2 Epq1=K*q1/r1 Epq2=K*q2/r2 K=1/(4πε0)=8.988x109 This gives me: Epq1=8.988x109*(3x10-6/3)=8988J...
47. ### Calculating electrical potential energy

Homework Statement Three equal point charges, each with charge 1.60μC , are placed at the vertices of an equilateral triangle whose sides are of length 0.600m . What is the electric potential energy U of the system? (Take as zero the potential energy of the three charges when they are...
48. ### Electron vs. Photon's electrical potential

Hi guys, After reading a paper about electron scattering, I became very interested. So if an electron is traveling in empty space, the electron's potential (according to the paper) is supposedly: http://www.flickr.com/photos/31694672@N07/ (I used flickr and Glui to post the particular...
49. ### Mathematical method in electrical potential ?

Mathematical method in electrical potential ?? Hi All, I need mathematical help from the topic electrical potential for lectures on physics by Richard Feynman. Need some help to understand mathematical method used here. question : 1) From electrical potential.png ( how this partial...
50. ### Given charge of uniform density. What is the electrical potential @?

Homework Statement Charge of uniform density 4.50nC/m is distributed along the circle of radius R. What is the electrical potential (relative to zero at infinity) at the centre of the circle? Answer: 254V Homework Equations electric potential: V=kQ/r The Attempt at a Solution Because the...