What is Method of images: Definition and 74 Discussions

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. M

    I Gauss' law, method of images, and force induced on conductor plates

    Hi, I would very much appreciate some guidance on the below. Consider a one-dimensional world as depicted in the attached figure. We have two (lets say positively charged particles enclosed by two conductor plates. One plate is at ##x=0##, the other at ##x=L##. The particles are at ##x_1## and...
  2. gunjanaga

    Looking for practice problems for "Method of Images" for charges

    Homework Statement: I am looking for practice problems for "Method of images of charges" Please help Relevant Equations: b=R^2/a q2=-R/aq1 I am preparing for IIT JAM
  3. J

    Method of mirroring - metal plates

    Hi, I'm having some trouble understanding how to solve this problem. I have a few questions: 1. I understand that I need to make an educated guess for the electric potential, where \(V_1\) is given by: V_1 = \frac{q}{4\pi\epsilon_0} \left(\frac{1}{r_1} - \frac{1}{r_2} + \frac{1}{r_3} -...
  4. T

    Line of charge and conducting sphere (method of images)

    I was thinking of using the sphere and point charge as an analog, but is quite diferent from what i have seen
  5. milkism

    Method of Images, combination of an infinite plane and a hemisphere

    Problem: I have done part a) in spherical polar coordinates. For part b) I thought it would be just: $$\sigma = -\epsilon_0 \frac{\partial V}{\partial r}$$ But I got confused by "You may want to use different coordinate systems .." So I assume partial derivative w.r.t to r is the spherical...
  6. J

    Method of Images from an earthed half cylinder and plane

    Hi, I want to solve the problem by method of mirroring and by using the electric field by doing superposition and then adding them up to use in Lorentz law to get the force. I have attached a figure that represents the problem. How do I know from the figure that $-p_l$ is from the...
  7. sinus

    I Grounded Means Zero Electric Potential: Exploring the Method of Images

    Can anyone explain to me why grounded means zero electric potential. I confuse what's the relation between infinite ground conducting plane and its electric potential (the method of images). I have a several question: 1. Why the conductor plane must be infinite, while in reality there's no...
  8. sinus

    I The Method of Images (Electromagnetism)

    Can anyone explain to me why grounded means zero electric potential. I confuse what's the relation between infinite ground conducting plane and its electric potential (the method of images). I have a several question: 1. Why the conductor plane must be infinite, while in reality there's no...
  9. josephsanders

    B Method of images and spherical coordinates

    I am finding the potential everywhere in space due to a point charge a distance 'a' on the z-axis above an infinite xy-plane held at zero potential. This problem is fairly straight forward; place an image charge q' = -q at position -a on the z-axis. I have the solution in cartesian coordinates...
  10. guyvsdcsniper

    Method of Images for a single point charge in a capacitor

    Disclaimer: This is not a repost. The problem wants me to calculate the force of a p.c. , that is isolated by itself (this p.c. is the only charge this problem starts with in this problem) inside a capacitor, a distance h/4 from the bottom plate. This is what I have though of so far but I...
  11. guyvsdcsniper

    Method of images between parallel plate capacitor

    Before I can find the force on q I must balance the charges. This problem starts of with -q and q inside the capacitor. I have added image charges on the opposite side of each plate. Would this work?
  12. GeniVasc

    Work done via induced charges in a grounded conductor

    I'm currently studying Method of Images in Griffiths book and in section 3.2 he introduces the method of images for a point charge at a distance ##d## from a grounded conducting plane at potential ##V = 0##. In subsection 3.2.3, Griffiths compute the energy of the real system and the image...
  13. P

    Programming a Diffraction Pattern by the (pseudo?) method of images

    I oriented a magnetic dipole perpendicular to the hole (parallel to the ŷ ŷ y^ŷ direction) with one end at it's origin and I get the following pattern I was really looking for something like this As you can see I'm getting almost the exact opposite of what I want since I'm going for...
  14. JD_PM

    Understanding how to apply the method of images to the wave equation

    Exercise statement Find the general solution for the wave equation ftt=v2fzzftt=v2fzz in the straight open magnetic field tube. Assume that the bottom boundary condition is fixed: there is no perturbation of the magnetic field at or below the photosphere. Solve means deriving the d’Alembert...
  15. sdefresco

    3-D Planar Method of Images Boundary Problem

    I understand the idea of the method of images, and its clever use of uniqueness to determine V(x,y,z) for non-trivial systems. My question now is simply about guidance for obtaining the effective "image" of this system, as it is clearly more complicated than the 2-plane analogue (in which there...
  16. B

    No problem, happy to help! Keep up the good work in your studies.

    Homework Statement The z = 0 plane is a grounded conducting surface. A point charge q is at (0,0,a), and charge 4q at (0,-2a,a). Calculate the potential in the region z > 0. Homework Equations V=∑kq/rThe Attempt at a Solution [/B] Use the method of images. V1 = kq/r+ + kq/r- V1=kq(1/sqrt(x^2...
  17. J

    Method of images for a line source

    Homework Statement Consider the curve C (image attached). C coincides with the real-z axis for $$|z| > a$$ and, in $$|z| < a$$ C coincides with the semi-circle $$|z| = a, =z > 0$$ In terms of simple singular flows, what is the image in C of a line source of strength 2πm lying at z = z_0, above...
  18. amjad-sh

    Method of images, charge q inside conducting sphere

    Homework Statement Using the method of images discuss the problem of a point charge q inside a hollow grounded conducting sphere of inner radius a.Find (a) the potential inside the sphere (b) induced surface-charge density (c) the magnitude and the direction of force acting on q is there any...
  19. E

    Method of Images two parallel pipes at potentials of 0 & +V

    Consider the scenario where there are two parallel conducting pipes of radius R separated by a distance d, with pipe 1 at a potential of -V and pipe 2 at a potential +V. I have seen from many sources that there is a very easy method of images solution to the potential outside the pipes, given...
  20. D

    Conceptual Laplace's/Poisson's Equation Solution Questions

    Homework Statement -You are given a solution to Laplace's equation inside of a cylindrical region radius R. -Show that by redefining the radial variable r as R2/r you get a solution for outside of R. -Grounded conducting cylinder at r=R. Using a linear combination of the solutions in the...
  21. T

    Deriving method of images

    Homework Statement the calculation can be considerably simplified by using the so called method of images. In this method, the electric field and potential produced by the induced charge distributed on the sphere can be represented as an electric field and potential of a single point charge...
  22. Z

    Method of images: infinite line of charge above plate

    Homework Statement An infinite line of charge with charge density λ is parallel to and a distance d above an infinite grounded conducting plate. What is the charge density σ that is induced in the plate? For simplicity, consider the line of charge to lie along the line x = 0. Homework...
  23. VMP

    Solving Method of Images Problem for Induced Charge

    Homework Statement We have a coordinate system (x, y, z). Two conducting plates 1 and 2 are parallel and lie in the x-y plane. Plate 1 is at height (x, y, 0) and plate 2 is at height (x, y, 4a), where a is an arbitrary constant. Between these two plates there are 2 charges +q and -q. Charge...
  24. F

    Method of images about a sphere with a dipole

    Homework Statement Hello everyone, I am new here and have a question regarding method of images in my electricity and magnetism class. I need help to even get the ball rolling. The question is as follows: a) What is the image of a dipole, oriented toward the center of the conducting sphere, if...
  25. A

    Calculating Electric Potential with Method of Images

    I'm solving a problem numerically where I have some charge density above an infinite, grounded conducting plane and want to determine the electrical potential at a given point. My intuition says that this is not simply given by the potential of the charge density above the plane, since this will...
  26. R

    Method of images: electric dipole and infinite plane

    Hello, a dubt arose while doing some exercise. If I have a charge q at a distance d from the above-mentioned plane, i can find the solution to the laplace equations (thanks to the uniqueness theorems) finding a collection of image charges that satisfies the boundary conditions. These conditions...
  27. davidbenari

    A question related to the method of images and uniqueness theorems

    My question is best illustrated by an example from a Griffiths book on E&M: "A point charge q is situated a distance ##a## from the center of a grounded conducting sphere of radius R (##a>R##). Find the potential outside the sphere... With the addition of a second charge you can simulate any...
  28. T

    The process of the method of images

    I am really confused that the whole process of the method of image. Suppose I have the + q near the infinite conducting plane which is grounded. My first question is: Is the conducting plane grounded before putting the +q or after putting the +q then grounded? The first question would lead to...
  29. M

    Green's function + method of images

    Hello, I'm trying to understand the application of Green's function to find the potential better. I apologize in advance if I start mixing things up a little. From what I understood and seen, we use this method (Green and method of images) in known symmetries (cylindrical/spherical/planar) and...
  30. Telemachus

    Electric Potential in Region z>0 Using Method of Images

    Hi there. The example to obtain the electric potential in the region z>0 by the method of images for a infinite grounded conducting plane, with a point charge q located at a distance d is a typical example of the application of the method of images. If we consider that the plane is located in...
  31. B

    Calculating Charge & Electric Energy Above a Plane

    Hello, I am stuck with this one. Your help/comments would be most appreciated. A charge "+Q" lies at a distance "d" above an infinitely large conducting plane. Applying the method of images, i found the right result that the total charge of the infinite plane is "-Q" and that the stored...
  32. L

    Method of images with dielectric

    Hi everyone I have an understanding problem concerning the method of images method Homework Statement Jackson uses this kind of problem in his textbook but I don't understand it. We have a charge q on the z axis at distance d. the dielectric constant is e1 when z>=0 and e2 when z<0. Now...
  33. D

    Method of Images: Grounded Conducting Sphere

    Homework Statement A point charge +q is situated a distance a from the center of a grounded conducting sphere of radius R. Find the induced surface charge on the sphere as a function of θ. Integrate this to get the total induced charge.Homework Equations σ=-εo*∂V/∂r Q=∫σ daThe Attempt at a...
  34. fluidistic

    Going through Jackson's book (electrodynamics, method of images)

    Homework Statement I would like to 1)Find the electric field in all the space in the following set up: There's an electric charge q in a region with dielectric constant ##\varepsilon _1## which is at a distance d from a plane that separates the space into 2 regions, namely the one of the...
  35. W

    Method of images to find potential near a grounded plane

    Homework Statement Have my E&M final tomorrow. Trying to work old test questions. Please check my answer for this question. Uniformly charged sphere of charge Q and radius R, center is a distance d above a grounded plane.Homework Equations V(r) in the interior of a sphere is given in the...
  36. T

    Calculating Electric Field b/w Grounded Conductors w/ Method of Images

    1. Homework Statement Two semi-infinite grounded conductive planes meet at right angles. In the region b/w the conductors, there is the plane with angle 45° having surface charge density σ. Using the method of images, find the field distribution in this region. (There is a picture included...
  37. N

    Method of Images- Force on Plane

    Homework Statement What is the force on an infinite conducting plane due to two point charges: a +2q located at a height 4h above the plane and a -q charge located at a height 2h above the plane, directly beneath the other point charge. Homework Equations The Attempt at a Solution...
  38. tomwilliam2

    Electrostatic potential using method of images

    Homework Statement There is a charge q, at a distance d from an infinite conducting plane (z=0). Determine the electrostatic potential drop between the z=0 and z=d. Homework Equations Ohm's Law DeltaV=-integral (E.dl) The Attempt at a Solution I know how to do this problem...
  39. A

    Explaining Why Total Charge Induced = -q for Image Problem

    Consider the classic image problem with a conducting plane and a point charge. After finding out the charge density on the plane we integrate to find out the total charge induced. It comes out to be "-q",where q is the charge outside- My book says "It comes out to be -q, as you can convince...
  40. M

    Solving Image Problems with Orthonormal Systems - M. Next

    Hello :) I would be very grateful if I get through with this bugging idea. When I started reading about it, the first example was: A point charge in front of a finite plane conductor. And I understood after some mathematical and geometrical procedure how it is okay to replace the finite plane...
  41. R

    Charge on a grounded conductor w/ method of images

    Why is it that whenever the method of images is used to solve for the induced charge on a grounded conductor in the presence of a point charge, the total charge is just the same as the image charge?
  42. R

    A dielectric + an infinite line of charge = use method of images

    Hi everyone, first time poster, long time reader (only because you're all so clever and I feel my contribution wouldn't be all that helpful haha). Homework Statement A dielectric (homogeneous, isotropic, with relative permativity \epsilon_{r}) is located in the region x<0. An infinite line...
  43. B

    Method of Images: Find Minimum Energy for Electron to Escape Metal Surface

    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...
  44. P

    Two Point Charge Force Calculation on Left Side

    Homework Statement Two point charges sit on either side of large grounded conducting plane. Give an expression for the force experienced by the charge on the left hand side. There is a neg charge on one side and positive charge on the other side. Homework Equations The electric...
  45. O

    Deriving Solutions with Method of Images

    Apply the method of images to derive the solution \displaystyle \phi(x,y,z) = \frac{z}{2 \pi} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \frac{f(x_0, y_0)}{((x - x_0)^2 + (y - y_0)^2 + z^2)^{\frac{3}{2}}} dx_0 dy_0 from \displaystyle \bigtriangledown^2 \phi (x,y,z) = 0 \phi(x,y,0)...
  46. O

    Method of Images - Green's Function

    Use the method of images to find a Green's function for the problem in the attached image. Demonstrate the functions satisfies the homogenous boundary condition.
  47. B

    Infinite Plane with Point Charge Above - Method of Images - Uniqueness Dogma

    Homework Statement You have point charge a distance "d" above infinite conducting plane held at V = 0. What is the potential when you remove charge to infinity? Homework Equations The Attempt at a Solution I think I incorrectly used Coulomb's law between the charge (+q...
  48. E

    Method of images& half a sphere

    Homework Statement http://img532.imageshack.us/img532/3751/39842434.png [Broken] Find the potential in all space for this configuration. Homework Equations ..basic electrostatics stuff, I guess. The Attempt at a Solution I can easily cancel the whole z=0 plane by placing a charge of...
  49. 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...