- #1
Kosta1234
- 46
- 1
- Homework Statement
- Grounded conductive shell
- Relevant Equations
- image method
Hello. I will be glad if someone can help me with this:
I've a grounded conductive shell with outer radius of ## R_2## and inner radius ##R_1##.
a charge ## Q ## is located inside of the shell, in distance ## r<R_1 ## , and a charge ## q ## is located in distance ## a > R_2 ## outside of the conductive shell.
The two charges are not located on the same axis and we don't know the angle between them.
What is the total charge on the shell?
My way of thinking is like this:
To split the problem to two main parts: the first one is a charge Q and radius ## R_1 ## shell. and the second is charge q and radius ## R_2 ## shell. I wanted to solve the laplace equation for each case - to figure out which image charges I should put so they would solve laplace equation and then, to solve this I would use: ## Q + q + Q_{image} = Q + q +Q_{shell} ##
to figure out the answer to the first part I used the method of image charges. I've ignored the fact that this is a shell with some given width, and found a potential that solved laplace's equation if the problem would be a charge Q and a shell with radius ## R_1 ##.
In this case I figured out that the image charge, which is located on the same axis that connecting charge Q with point (0,0,0) is:
## Q' = -Q \frac {R_1}{r} ##
the same thing with the second part:
## q' = -q \frac {R_2}{a} ##
so
## Q_{image} = -Q \frac {R_1}{r} -q \frac {R_2}{a} ##
it means that
## Q_{shell} = -Q \frac {R_1}{r} -q \frac {R_2}{a} ##
But I saw the answer, and she is:
## Q_{shell } = -Q -q \frac {R_2}{a} ## .
Where I've been wrong?
Thank you.
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