A method to solve certain differential equations on a domain by putting image sources outside the domain to fulfill [boundary-conditions] on the boundary. Common applications can be found in [electrostatics], [magnetostatics] or [acoustics].
Questions tagged [method-of-images]
138 questions
17
votes
4 answers
What is the justification for the method of images in electrostatics?
The method of image charges is a well-known and very useful tool for solving problems in electrostatics.
Unfortunately, when I was taught this method, it was presented simply as an algorithm. No real physical justification was given for its usage,…
Noldorin
- 7,547
8
votes
2 answers
Question about the Green's function for a conducting sphere
In Jackson's Classical Electrodynamics, he gives the Green's function for a conducting sphere with Dirichlet boundary conditions as
$$ G(\mathbf{x},\mathbf{x}^\prime) = \frac{1}{|\mathbf{x} - \mathbf{x}^\prime|} - \frac{a}{x^\prime\left|\mathbf{x} -…
8
votes
1 answer
Charge over 2 layer dielectric, image method
If I have a charge $Q$ located over a 2 layer dielectric as represented:
According to the image method: the charge $Q'1$ will be located at a distance $h_1$ under the first interface and the $Q'2$ will be located at a distance $h_2$ under the first…
6
votes
2 answers
A point electric charge in an angle sector: does the Green's function expansion simplify to the method of images if the angle is right?
Suppose that you're doing electrostatics in two dimensions (or, equivalently, in 3D with translation invariance along $z$) and you're studying the response to a point charge in an angle sector of opening angle $\alpha$, i.e. in the…
Emilio Pisanty
- 137,480
6
votes
3 answers
Method of image charge for cylindrical conductor
I am simply puzzled that only for spherical and planar conducting surfaces the method of images is applied. Is it (really) impossible to find image charge or charge distribution which can simulate the behaviour of potential in the volume of…
The Imp
- 1,036
6
votes
4 answers
When to use method of images in electrostatics?
I am a bit confused about when to use the method of images in E&M? For example, in Griffiths' Introduction to Electrodynamics, Example 3.2, the problem reads:
A point charge $q$ is situated a distance $a$ from the center of a grounded conducting…
Guest
- 375
5
votes
2 answers
Using the image charges method to find the electric field
The following is a question from a tutorial in my Physics 2 course about conductors and the Method of image charges.
We are given two infinite perpendicular and grounded plains.
The first plain is in the $X-Z$ plain and the second one is on the
…
Belgi
- 525
5
votes
2 answers
Method of image charges for more than one surface
I would like to better understand the method of image charges for more than one planar surface. I know that the whole objective is to satisfy the boundary conditions, and thus this can be used as a check for any potential solution. However I would…
Tom
- 992
5
votes
2 answers
Conservation of charge and method of images
Consider the typical problem,
You have a conducting sphere of charge $Q$ and a point charge $q$ a certain distance away, what is the force on the point charge?
The solution is a simple application of the method of images, but in Griffiths part of…
KF Gauss
- 8,314
5
votes
1 answer
Can I use method of images for a point charge outside a solid dielectric sphere?
My question arised while solving Classical Electrodynamics(J. D. Jackson) Pro 4.9a
Find a potential at all points in space for a point charge $q$ located in a free space a distance $d$ from the center of a solid dielectric sphere of radius $a(a <…
Liberty
- 490
5
votes
1 answer
Method of images for intersection of two planes
Vanderlinde's Classical Electromagnetic Theory discusses the method of images, with examples given for intersecting infinite conducting (half) planes. In particular, the "kaleidoscope" effect of alternating image charges for planes intersecting at…
Bob Arthur
- 101
5
votes
6 answers
Method of image charges for a point charge and a non-grounded conducting plane
I know how to solve Laplace's equation for a point charge in front of a grounded conducting infinite plane. But I want to know what happens (both physics and math) when the infinite conducting plane isn't grounded, or is connected to a potential…
Alireza
- 484
4
votes
1 answer
Blasius's theorem - Fluid Dynamics
So my fluid's professor gave us an exercise where we had to calculate the force exerted on a wall by a vortex separated a distance $d$ to it. By the method of images we can build the complex potential…
adricello05
- 117
4
votes
0 answers
Understanding Green's function in the mirror charge method
Initially I want to point out that there are many way as to how we can define the green's function in vacuum or when other objects are taken into consideration, and the same goes for the Potential in the case when we consider conducting objects, or…
imbAF
- 1,912
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4
votes
1 answer
Location of mirror charges
I was reading about the method of images from Griffiths and I was thinking about a situation where a charge is kept inside a spherical cavity of a conducting shell rather than placing it outside a conducting shell.
Here the sphere is not grounded.…
Aditya Dev
- 661