Method of images Definition and 75 Threads

The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which the domain of the sought function is extended by the addition of its mirror image with respect to a symmetry hyperplane. As a result, certain boundary conditions are satisfied automatically by the presence of a mirror image, greatly facilitating the solution of the original problem. The domain of the function is not extended. The function is made to satisfy given boundary conditions by placing singularities outside the domain of the function. The original singularities are inside the domain of interest. The additional (fictitious) singularities are an artifact needed to satisfy the prescribed but yet unsatisfied boundary conditions.

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  1. T

    Method of Images in Electrostatics

    Homework Statement A point charge q is held a distance d > a below the centre of a large spherical conductor of radius a. Show that, if the spherical conductor is earthed, the potential outside the sphere may be found by placing an image charge at a distance c=a2/d from the centre of the...
  2. W

    Method of images for two charges and two planes

    Homework Statement Consider two charges, +q each, placed between two grounded plates at a distance d along the z-axis from each plate. thus, the potential V(x,y,-d) = 0 and V(x,y,d) = 0 and the charges are placed at (+R/2,0,0) and (-R/2,0,0) being a distance R apart. Draw the location and...
  3. P

    Method of Images: How does the uniqueness theorem apply?

    [b]1. Point charge in the presence of a grounded conducting sphere given the boundary conditions phi(x)=0 at r=a (V=0) and at r=infinity (V=0) [b]2. The equation I used phi(x)= (q/abs(x-y))+(q'/abs(x-y))=(q/abs(x*nhatsubx-y'nhatsuby))+ (q'/abs(x'*nhatsubx-y'*nhatsuby') [b]3. The...
  4. S

    Diffusion Equation by Method of Images

    Homework Statement I need help in solving a problem I was assigned from Numerical Methods for Physics, 2nd Ed., by Garcia. We are asked to create a solution, by hand, for the diffusion equation, using the method of images. In particular, we have a 1-dimensional bar, centered at x = 0, of...
  5. U

    Method of Images (Electrostatics)

    Homework Statement A grounded spherical shell has inner radius of 1m. and outer radius of 2m. Q1=1 Coul. is located at x=0.5m and Q2=-2 Coul. is located at x=4m, respectively. Homework Equations Find the charge system to find the potential outside the shell. Find the charge system to find...
  6. S

    Method of Images - Need a hint

    Homework Statement A conducting sphere of charge Q and radius A is located at a distance D from the sphere's center to an infinite, grounded, conducting plane. Ultimately, I would like to find the capacitance, but that is simple once I find the potential. So the question is:How does one...
  7. P

    Method of Images Question (Concave Geometries)

    I've been working with image charges for a while now, and I have noticed that I haven't been able to find a single discussion on the use of image charges for concave geometries (i.e. a charge on the "inside" of a catenary shaped curved conducting plate, see attached picture). Has anyone worked...
  8. V

    Why does the method of images use a distance of 2x instead of just x?

    Homework Statement A point charge +q is initially at distance x from a conducting plane of infinite extent and held at zero potential. Find the work done in moving the charge to an infinite distance from the plane. Hence find the minimum energy an electron must have in order to escape from a...
  9. K

    Method of images in Griffiths' text

    In Griffiths' text "Introduction to electrodynamics", p.125, how does the author get (3.15) and (3.16)? I try for an hour to deduce the relation with geometry, but still can't get that.
  10. W

    Method of images with infinite, earthed, conducting plane

    Hello guys, I'm having some trouble getting my head around the method of images, partly due to confusing notes and things. If I have a charge +q at a fixed point (0,0,a) above a conducting plane that is held at zero potential, it is said that the plane can be replaced with a charge of -q...
  11. B

    Diffusion eq. with periodic BC using method of images

    Homework Statement Considering the periodic boundary conditions (given below) I am supposed to find the solution T(x,t) with the initial condition T(x,0)=\delta(x) Also I am limited to use method of images so I can't use separation of variables unfortunately. Homework Equations The boundary...
  12. Somefantastik

    Green's Function using method of images

    Homework Statement \Omega = \left{ \left( x,y,z \right) :,0<z<1 \right} Need to find Green's function using the method of images. Homework Equations none The Attempt at a Solution I can see that I will need an infinite sequence of images at each plane z = k, k = 0, +/- 1, +/- 2,... to...
  13. L

    Method of images and spherical shell

    A grounded & conducting spherical shell of outer radius M and inner radius N has a point charge Q inside the shell at a distance r<M from center. Using method of images, find the potential inside the sphere. Could I just use the superposition of charge and point charge? \phi(r) =...
  14. S

    Method of Images: Infinite, charged wire above a grounded plate

    Homework Statement Given an infinitely long wire, with charge density \lambda, parallel to and a distance d above an infinite, grounded, conducting sheet, what is the potential, V(x,y,z) above the sheet? What is the induced charge on the sheet? Homework Equations The Attempt at a...
  15. N

    How Does Grounding Affect the Electric Field of a Charged Plate?

    The setup is: Suppose that we have a point charge q held a distance d from an infinite, grounded, conducting plate. Let the plate lie in the xy-plane, and suppose that the point charge is located at coordinates (0, 0, d). What is the scalar potential above the plane? The solution to this...
  16. D

    How does the method of image charges work between two conducting surfaces?

    I'm reading about the method of image charges at http://en.wikipedia.org/wiki/Method_of_image_charges The page describes a charge located above a single conducting surface. What happens if the charge is between two conducting surfaces? Does the bottom plate, along with the imaginary...
  17. W

    E&M Method of Images: Amplitude Adjustment?

    The method of images exploits the fact any linear combination of solutions to a differential equation is also a solution, and the fields and potentials from a point source satisfy all relevant diff eq's, assuming the boundary conditions are met. However, a scalar multiple of any solution is...
  18. P

    Method of images to solve green's function problems

    How does the method of images work? I can see why it works (by going back to the form of the Green function and differentiating) but don't see how useful it is to solve problems. At the moment I am basically memorising the different images for each boundary condition which I am sure is not the...
  19. V

    How Does the Method of Images Solve Poisson's Equation in All of Space?

    Dear all, I have some difficulties in understanding to use the method of images to solve Poisson's/Laplace's equation with boundary values. I understand that the Uniqueness theorem(s) enables this method. In this method we use image charges and setup a different configuration without...
  20. S

    How Do You Determine Image Charges for Angled Conducting Planes?

    Homework Statement To conducting planes are placed at an angle 60 degrees to each other. A point charge q is placed on the line bisecting this angle at a distance a/2 fro each plane. Find the image charges and the resulting potnetial Homework Equations V(0,0) = 0 V(x,0) = 0...
  21. S

    Method of images and infinite conducting sheet

    Homework Statement An infinite conducting sheet has a hemispherical bubble of radius a. (Refer to the diagram) 2. The attempt at a solution ok i know the boundary conditions should be (Phi refresents the potential) And we are working in CGS units... units with which i am not entire...
  22. S

    Electromagnetics - Method of Images ?

    Electromagnetics - Method of Images ? Hello all, I am in the process of preparing for a entrance examination. In the course of studying I came across this problem that I just can not figure out. Here it is: A perfectly conducting plane is located in free space at x=4, and a uniform inifinte...
  23. S

    Calculating Capacitance & Inductance of Cylindrical Conductors

    We have to find the capacitance and inductance of a pair of cylindrical conductors of radius r and at a distance d b away from each other. I get the following expressions C = 2Pi*epsilon0/ln(b/a) L = Mu0/2Pi *ln(b/a) We now have a cylindrical conductor a distance d above an infinite...
  24. quasar987

    Using the Method of Images to Find the Force on q

    The situation is illustrated in the attachment. I try to find the force on q by the method of images. I know that the potential is 0 at x=R and at infinity, and I know that The potential obeys a certain Poisson equation between those points. I will try to put a charge q' somewhere at x<R that...
  25. N

    Solving Method of Images Problem for Infinite Conducting Cylinder

    Hello, I am requiring some help on a problem on method of images. The problem is, you are given a infinitely long conducting cylinder of radius a, with charge density per unit length lambda (I'll use the symbol Y) which is placed with its axis a distance d from an infinite conducting plane at...
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