Image charges Definition and 25 Threads

The method of image charges (also known as the method of images and method of mirror charges) is a basic problem-solving tool in electrostatics. The name originates from the replacement of certain elements in the original layout with imaginary charges, which replicates the boundary conditions of the problem (see Dirichlet boundary conditions or Neumann boundary conditions).
The validity of the method of image charges rests upon a corollary of the uniqueness theorem, which states that the electric potential in a volume V is uniquely determined if both the charge density throughout the region and the value of the electric potential on all boundaries are specified. Alternatively, application of this corollary to the differential form of Gauss' Law shows that in a volume V surrounded by conductors and containing a specified charge density ρ, the electric field is uniquely determined if the total charge on each conductor is given. Possessing knowledge of either the electric potential or the electric field and the corresponding boundary conditions we can swap the charge distribution we are considering for one with a configuration that is easier to analyze, so long as it satisfies Poisson's equation in the region of interest and assumes the correct values at the boundaries.

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  1. bob012345

    Infinite Number of Image Charges?

    Consider two opposing mirrors. If they are exactly parallel planes I think there is only a single image in each but if they are slightly angled there appears an "infinite" number of reflections. Similarly, suppose we have grounded conducting planes instead of mirrors with a charge in between...
  2. Othman0111

    Charge Between two conductors & The Method of Image Charges

    Homework Statement Homework Equations The Attempt at a Solution I'm sure my solution is wrong because of Φ(z=0) ≠ 0 I searched the internet for a similar problem but I couldn't. Any help will be appreciated.
  3. G

    Image Charges Purcell Discussion

    Hi everyone, I have a question (or three) regarding Purcell's discussion of image charges, in pg 137-139 of the third edition of his EM book. He goes over the classic image charge example: a plane held at zero potential, and a charge Q a distance h above it. I'm fine with everything he...
  4. B

    How Do You Compute the Electric Potential Using the Method of Image Charges?

    Hi, I am learning about the method of image charges, but am struggling to sufficiently justify my answer. It appears to be correct, though it quite possibly isn't... 1. Homework Statement (please see attached item) Two semi-infinite grounded conducting planes (the shaded region in the...
  5. A

    Why Does the Mirror Charge Method Double the Potential Energy?

    Hi everybody, The situation is the classic one: a point charge q+ in a distance d above a conductor plane grounded: The conductor is grounded so V = 0, for z = 0. Also, far away from the system (x2 + y2 + z2 >> d) V --> 0 The argument to replace it for a q- charge seems perfect to me. What I...
  6. C

    Is a Closed Form Solution Possible for Charge Near a Conductive Slab?

    Just wondering if anybody knows if it is possible to write a closed form solution for this problem, or how to tackle it. Image charges?
  7. R

    Is a Grounded Plane Electrically Neutral?

    Consider the following configuration: a grounded plane (very thin and with an infinite surface) and a positive (not important) point charge above it. What does grounded really mean? Can't I assume that it is neutral and it has infinitely many positive and negative charges? Because of the...
  8. diegzumillo

    Inverse of method of image charges

    Hi all What if instead of charges and a surface, we were given a set of charges and image charges and have to find the surface, how would you do that? This is actually part of my homework but I'm pretty sure he doesn't want us to prove it mathematically (the case is obviously a sphere) so I...
  9. S

    Point charge above infinite conducting plane

    This question seems to come up often, but I cannot find a satisfying explanation. There is a point charge +Q some distance above an infinite conducting plane. Supposedly, the electric field below the plane must be zero. I have trouble understanding why this is true. The total charge on the...
  10. R

    Image Charges and a hollow conducting sphere

    Homework Statement Hi! Bear in mind, before shooting me down, that I'm very new to electrostatics and extremely (i.e. today) new to the method of image charges, and all my learning is dodgy book-learning and not learning from asking the learned questions. This said, I just want my...
  11. A

    Help Needed: Calculating Force Using Image Charges

    Hi, I'm trying to use image charges to find the force that apply on the following particle (on the attachment) , but it seems that I do something wrong - F=2q^2/(2a^2)-2cos(60)q^2/a^2 The gray section have 0 potential, so I've tried to put image charges like it is in the second attachment...
  12. M

    Electric Field at Surface of Earthed Sphere (using image charges)

    "A charged sphere is a distance d from the centre of an earthed sphere conducting sphere of radius a. An image charge (q') for this system is located at a distance b from the centre of the sphere where: q'= -(aq/d) and b=(a^2)/d Calculate the expression for the Electric field at point p...
  13. Saitama

    Is There an Easier Method to Solve Problems Involving Image Charges?

    Homework Statement (see attachment) Homework Equations The Attempt at a Solution I think i need to use method of image charges here but if i do that, i need to place infinite fictitious charges and finding the electric field at the surface of any of the plate would be very...
  14. L

    Question regarding Image Charges

    Hey, I have a question about the use of image charges to solve problems, Once you have determined the potential of the problem by including image charges you have to check if the potential describes the physics properly, so if you have an infinite earthed conducting sheet with chat q...
  15. K

    (Image Theory) Boundary conditions and how many image charges do i need?

    Homework Statement An electrostatic point charge of 1 Coulomb (C) placed symmetrically between two infinitely/perfectly conducting parallel plates. These two infinitely large conducting plates are parallel to the yz plane.The region between the two plates is designated as “Region A.” Starting...
  16. P

    Image charges of a 30 degree corner

    Homework Statement I just want to make sure I'm doing this right. okay so you have a conducting corner of angle 30 degrees. How many image charges are there, I just need to sketch it. Homework Equations The Attempt at a Solution my book sucks only explaining it for a 90 degree...
  17. J

    Calculating Image Line Charges for Multiple Wires

    I have the below figure I took from my textbook from a section that explains how to calculate the capacitance of two transmission wires using image line charges. My question is that if I add two more conductors like shown below, how would it affect the line image charges? I'm not sure...
  18. R

    Method of Image Charges - Range of validity of solutions

    When using the method of image charges to solve a problem in electrostatics, how do we determine the volume of space in which our solution is valid? And how do we find the solution outside this volume? To be more specific, let's consider two examples. The first is the classic point charge above...
  19. E

    How Do You Solve for the Potential Outside a Dielectric Half-Space?

    A point charge q is a distance d from a dielectric half-space (z < 0). We will solve for the potential outside of the dielectric, in the region z > 0. (a) Away from the point charge, what equation does V satisfy? Find the boundary conditions at the dielectric surface. (b) Find an image...
  20. A

    How Does a Dielectric Half-Space Affect the Potential of a Nearby Point Charge?

    Homework Statement A point charge q is a distance d from a dielectric half-space (z < 0). We will solve for the potential outside of the dielectric, in the region z > 0. (a) Away from the point charge, what equation does V satisfy? Find the bound- ary conditions at the dielectric...
  21. L

    Method of image charges: any extension for oscillating fields?

    I was wondering if the "Method of image charges" could be extended even partly or approximately to oscillating charges. I am not considering nearly-static problems, but really radiating problems. After all, the Poisson equation and the wave equation are rather close ! Therefore, I thought...
  22. C

    Calculating the Force on +q Charge Using Image Charges

    Homework Statement The configuration is that there is a charge +q a distance 3d on the z axis and a charge -2q a distance d on the z axis. The xy plane is a grounded conductor. Find the force on the charge +q. Homework Equations I've place image charges: -q at z=-3d and +2q at z=-d. the...
  23. T

    Where Should I Place Image Charges for a Conducting Wall and Charged Sphere?

    Homework Statement We have a conducting and grounded wall for z<0, so \Phi=0 for z<0. In front of this wall, we place a homogeneous charged sphere with radius R and total charge Q. The center of the sphere has a distance of a to the front of the wall...
  24. S

    Ooo template Method of image charges

    Homework Statement Two semi-infinite grounded plane conductors that intersect at the origin, with an angle of 60 degrees between them. A point charge of q is located some distance from the origin, and bisects the angle between the two conductors, where would the image charges be and what...
  25. Reshma

    Where can I find the image charge for a point charge near conducting surfaces?

    Someone's got to help me on these two. 1)Two semi-infinite grounded conducting planes meet at right angles. In the region between them, a point charge q is kept such that it is at a distance of 40cm from each of the two planes[i.e.(40,40)]. Find the position of its image charge/charges...
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