electric potential Definition and Topics - 112 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. J

    Electric Potential of point outside cylinder

    Edit: Below is my work but i believe i have chosen the wrong values of the separation vector in the s direction. Any ideas as to what it should be?
  2. A

    Calculating the force on an electron from two positive point charges

    So this is more of an intuitive question rather than a mathematical one. I present the problem. Assume I have 2 charges of charge +q at a distance r from each other on the z axis. Position of two charges is (0,0,r/2) and (0,0,-r/2). Assume now that I want to calculate the force these two...
  3. Z

    Potential Gradient for individual charges and parallel plates?

    In my book, the potential gradient for a charge placed anywhere in space is defined as: E = -V/r HOWEVER, for parallel plate (capacitors) the potential gradient is defined as E = V/d (V being the potential difference). How come there's no negative sign for the potential gradient of the parallel...
  4. G

    A Laplace eq. in cylindrical coordinates and boundary conditions

  5. D

    Deriving electric and vector potential

    1- Write down the complete MAXWELL equations in differential form and the material equations. 2- An infinitely extensive area is homogeneously filled with a material with a location-dependent permittivity. There are charges in the area. Give the Maxwell equations and material equations of...
  6. A

    Who invented electric potential and why?

    Why was that concept necessary ?, I know there's also a gravitational equivalent of this concept I couldn't find anything on google Thanks Daniel
  7. Athenian

    Finding the Monopole and Multipole Moments of the Electric Potential

    My first attempt revolved mostly around the solution method shown in this "site" or PowerPoint: http://physics.gmu.edu/~joe/PHYS685/Topic4.pdf . However, after studying the content and writing down my answer for the monopole moment as equal to ##\sqrt{\frac{1}{4 \pi}} \rho##, I found out the...
  8. B

    Electric Potential inside an insulating sphere

    I used the potential at the surface of the sphere for my reference point for computing the potential at a point r < R in the sphere. The potential at the surface of the sphere is ## V(R) = k \frac {Q} {R} ##. To find the potential inside the sphere, I used the Electric field inside of an...
  9. D

    Voltage using different references

    The problem is for a solid sphere uniformly charged with Q and radii R. First I calculated taked ##V(\infty)=0##, giving me for : $$ \begin{align*} V(r)=&\frac{3Q}{8\pi\varepsilon_0 R}-\frac{Q}{8\pi\varepsilon_0 R^3}r^2\qquad\text{if $r<R$}\\ V(r)=&\frac{Q}{4\pi\varepsilon_0 r}\quad\text{if...
  10. Kaushik

    Does potential drop when a charge flows through a wire w/ 0 resistance?

    Let us connect a battery of potential difference V to a wire. There is no resistance. Nothing! Now the battery creates some potential difference and the charges in the conducting wire move due to the Electric field created in the conductor by the battery. So, as the charge moves, its potential...
  11. F

    Charge rearrangement on conducting spheres

    Hi, I think this problem is solved in exactly as a similar problem where the two spheres are very far apart and connected by a very long thin conducting wire. I'm trying to explain this in words, since LaTeX does not seem to work any more (for some reason LaTeX syntax is not replaced by maths in...
  12. CrosisBH

    Trouble with Electric Potential Boundaries (Computational Physics)

    This is in python: #ELECTRIC POTENTIAL from mpl_toolkits.mplot3d import Axes3D from matplotlib import cm import numpy as np import matplotlib.pyplot as plt dx = 0.1 dy = 0.1 xrange=np.arange(-1,1,dx) yrange=np.arange(-1,1,dy) X,Y = np.meshgrid(xrange, yrange) max_dV = 10e-5 blockRadius = 3...
  13. K

    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...
  14. Tryhard314

    Parallel plates potential

    Summary:: if Plate A had a potential of 9V, This means as We approach a unit charge from +Infinity to A we have to do this precise amount of work Now we remove plate A, And replace it with plate B that has a potential of -9V Again that means to go from +Infinity To B we actually gain energy, or...
  15. Tryhard314

    Salt water and potential difference

    Imagine a container of salt water at 0V (Relative to ground),Now you've put in it 2 electrodes,one at +500V (Electrode A), The other at +250V(Electrode b), Normally positive ions should go to the negative electrode , and Negative ions should go to the positive electrode , But in our example the...
  16. adamaero

    Electric energy density in the dielectric of a coaxial cable

    V(ρ) = V_o*ln(ρ/0.0018)/ln(45/180) (Attached picture is where the unit vector of r is really ρ.) In cylindrical coordinates ∇V = ρ*dV/dρ + 0 + 0 ∇V =derivative[V_o*ln(ρ/0.0018)/1.386]dρ ∇V = V_o*0.0018/(1.386*ρ) E = V_o*0.0012987/ρ Work = 0.5∫∫∫εE•E dv Bounds: 0.0018 to 0.00045 m D = εE =...
  17. kmm

    Potential of a grounded conductor in the presence of an external charge

    If we set the potential at infinity to be zero, we find that the potential of a grounded conductor is V=0. The conductor being grounded has no net charge and produces no external field, so I understand why in that situation we would say the potential of the conductor is zero. However, in...
  18. AndresPB

    Electric Field from its Potential of a Half Circle along its Z axis

    So I figured out the potential is: dV = (1/(4*Pi*Epsilon_0))*[λ dl/sqrt(z^2+a^2)] . From that expression: We can figure out that since its half a ring we have to integrate from 0 to pi*a, so we would get: V = (1/(4*Pi*Epsilon_0))*[λ {pi*a]/sqrt(z^2+a^2)] In that expression: a = sqrt(x^2+y^2)...
  19. S

    Potential at the origin due to an infinite set of point charges

    Summary: Potential at origin of an infinite set of point charges with charge (4^n)q and distance (3^n)a along x axis where n starts at 1. From V=q/r, we find Vtotal=sum from 1 to infinity of (4/3)^n(q/a), which diverges. There cannot be infinite potential because there is a finite electric...
  20. cianfa72

    Galvanic cell - open circuit voltage and EMF

    Hi, having not a deep knowledge of electrochemistry I've some doubts about processes involved in a galvanic cell. Take for instance a Zn/Cu Daniell cell for which E0cell is 1,10V. That means emf for it is 1,10V. Starting to read from how battery works I had a first understanding of how...
  21. T

    Capacitance and induced charge of a spherical Capacitor + dielectric

    I) For the first part I used: ##V = - \int E ds = \int_a^c \frac{1}{4\pi\epsilon_0} Q /r^2 dr+ \int_c^{c+d} \frac{1}{k} \frac{1}{4\pi\epsilon_0} Q /r^2 dr + \int_{c+d}^b \frac{1}{4\pi\epsilon_0} Q /r^2 dr ## And by using ##C = Q/V## We get an answer which is somehow large for writing here...
  22. cianfa72

    Electric potential difference between a battery's + terminal and the ground

    Hi, I've a question about electricity in the following scenario: consider an accumulator (e.g. a 9V battery) and an analog/digital voltmeter having a probe connected to the accumulator + clamp and the other to the ground (for instance connecting it to a metal rod stuck in the ground). Do you...
  23. Miles123K

    Calculating the charge of two concentric conductive spheres

    Homework Statement The solution to this problem is B, and I was able to get the answer by calculating the total potential at ##r = 2a##, however, what I don't seem to understand is why must the voltage be calculated at ##r=2a## but not ##r=3a##. Homework Equations ##V(r) = - \int_a^b E(r)...
  24. L

    Potential Energy and Potential -- Systems versus Particles

    When I first learned about these subjects, I did what was intuitive to me and treated particles as if they carried potential energy. I would do this similarly for rigid bodies where I would also treat them as a particles with their body's mass at the center of mass. This wasn't helped by...
  25. L

    At what point is Electric Potential zero

    1. The problem statement Two charges of 3μC and -2μC are placed 2cm apart. At what point along their connecting line is electric potential zero? Homework Equations Electric potential superposition Φ=Φ1-Φ2 since q2 is negative Φ=kq/r^2 The Attempt at a Solution Let’s say the charges are on the...
  26. P

    Wire surrounded by a linear dielectric in a uniform E field

    Homework Statement We have an uncharged, conducting wire with radius a. We surround it by a linear dielectric material, εr, which goes out to radius b. We place this in an external electric field, Eo. Homework Equations We have electric potential inside (a < s < b) Vinbetween=Acosφ +...
  27. P

    Calculating the electric potential

    Homework Statement We have the cross section of a metal pipe that has been split into four sections. Three of the sections have a constant electric potential, Vo. The fourth section is grounded so electric potential is zero. We are looking for electric potential inside and outside of the pipe...
  28. B

    Electric Field and Potential in a conductor

    So in my textbook (Introduction to Electrodynamics by Griffiths) it said that inside a conductor, the electric field E would have to zero, since if it wasn't the free charges would move accordingly and create a electric field that cancels the original field. But in a question that soon followed...
  29. V

    How do I calculate the potential created by a dipole

    Homework Statement I'm given that there is a positive charge of 1 nC at x=0.25 m and a negative charge of -1 nC at x=-0.25 m. I've calculated the potential created at different points along the x-axis by the positive charge and the negative charge using the formula, $$V=\frac{kq}{|r|},$$ where...