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.
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...
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
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} -...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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.
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...
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...
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...