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Question about concentric conductors

  • #1

Homework Statement


Three insulated concentric spherical conductors, whose radii in ascending order of magnitude are ##a, b, c##, have charged ##e_1, e_2, e_3## respectively, find their potentials and show that if the inner most sphere is grounded, the potential of the outermost is diminished by:

##\frac{a}{c} ( \frac{k e_1}{a} + \frac{k e_2}{b} + \frac{k e_3}{c} ) ##.


Homework Equations



##k = \frac{1}{4 \pi \epsilon_0}##

The Attempt at a Solution


[/B]
The potentials in each region are ##V_I = \frac{k e_1}{r} + C##, ##V_{II} = \frac{k (e_1 + e_2)}{r} + D##, and ##V_{III} = \frac{k (e_1 + e_2 + e_3)}{r} + E##, where ##C, D## and ##E## are integration constants. Setting the potential at the innermost sphere to ##0##, we solve for ##C##, giving us ##V_{III} = \frac{k e_1}{r} - \frac{k e_1}{a}##. Ensuring continuity @ ##b## and ##c##, I finally get ##V_{III} = \frac{k (e_1 + e_2 + e_3)}{r} - (\frac{e_3}{c} + \frac{e_2}{b} + \frac{e_1}{a})##. I just don't see how we get the factor of ##\frac{a}{c}## on the outside. Help is greatly appreciated.
 

Answers and Replies

  • #2
BvU
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Hello Jason,

I read the exercise as consisting of two parts: a) find the potentials, and b)ground the inner sphere and ... etc.
 
  • #3
Hello Jason,

I read the exercise as consisting of two parts: a) find the potentials, and b)ground the inner sphere and ... etc.
Oops, sorry you're totally right. I left the potentials in that form because you can't solve for ##C##, ##D##, and ##E## without knowing the potentials on each surface. Is this the wrong way of approaching the problem?
 
Last edited:
  • #4
BvU
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you should be able to solve part a using potental zero at infinity
 

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