Second uniqueness theorem

  • Thread starter pardesi
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Main Question or Discussion Point

it states that in a given volume V surrounded by conductors or for that matter infinity if the charge density [tex]\rho[/tex] and the charge on each conductor is fixed then the electric field is uniquely determined in that volume V

Can someone use this find the field in certain situations.
For Example consider this classical situation where in an uncharged conductor has a cavity of arbitrary shape inside it which has a point charge q inside it .The question is to find the net field outside it .
Ofcourse the answer is shielding by the metallic sphere ?
Can someone prove this using the uniqueness theorem .I have a proof in mind but i am unsure of it?
 

Answers and Replies

pam
455
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What does "net field" mean?
The field outside the conductor will be the same as that outside a solid conductor with total surface charge q. The field outside such a conductor depends on its shape.
By Gauss's law, the surface integral of E is known.
 
339
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What does "net field" mean?
The field outside the conductor will be the same as that outside a solid conductor with total surface charge q.
this is what i am asking u to prove.
also that the charge q is uniformly distributed
 
pam
455
1
The surface charge on the conductor has to be q, by conservation of charge.
The surface charge will not be uniform, unless the outer surface is spherical.
 
339
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it is a sphere ....
even that doesn't 'prove' that the charge is uniform
 
pam
455
1
The title of your question was "uniqueness theorem". Use it.
If a spherically symmetry E outside the conductor satisfies all BC, then it is the unique solution. QED.
 

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