Field & Charge Distribution of Conducting Sphere & Shell

[assaftolko]

Homework Statement

A solid conducting sphere with radius of R1 and charge of 3Q, is placed in the center of a thin conducting spherical shell with inner radius of R2 and outer radius of R3, charged with -Q

what is the field for r<R1, R2>r>R1, R3>r>R2, r>R3 and what is the charge distrubution for the sphere and the shell?

Well I'm quite sure that the field inside the sphere is 0, and when R2>r>R1 the field is like of a 3Q point charge in the middle of the sphere. and also when r>R3 it's the field of a point charge 2Q in the middle of the sphere. but what hapeens in R3>r>R2? Although this segment describes points inside the conducting shell I don't think the field is 0... but I don't know if I'm right because you always have to assume that the field inside a conductor is 0 right? (under electro-static conditions).

Also what is the charge distrubution? How can I know it? I know that inside the sphere all the charge will be on the surface... but what happens with respect to the 2-surfaced shell?

 

[haruspex]

what hapeens in R3>r>R2? Although this segment describes points inside the conducting shell I don't think the field is 0... but I don't know if I'm right because you always have to assume that the field inside a conductor is 0 right? (under electro-static conditions).

The field inside a conductor is indeed guaranteed zero when there's no current. If there were a field then charges would immediately flow.

Also what is the charge distrubution? How can I know it? I know that inside the sphere all the charge will be on the surface... but what happens with respect to the 2-surfaced shell?

By the same reasoning, all charge will be on the surfaces of the conductor. You just have to figure out how much on each of the two surfaces (so that there is no field within the conductor body).

 

[assaftolko]

The field inside a conductor is indeed guaranteed zero when there's no current. If there were a field then charges would immediately flow.
By the same reasoning, all charge will be on the surfaces of the conductor. You just have to figure out how much on each of the two surfaces (so that there is no field within the conductor body).

Ok so indeed the field in R3>r>R2 is 0... but how can I really know the charge distrubution within the conducting shell? I really don't know... maybe all the charge is near the inner surface? maybe it's all near the outer surface? what difference does it make?

 

[haruspex]

As I said, all the charge is on the surfaces. Suppose the charge on the inner surface is H. So you have 3Q on the central sphere, H on the inner surface of the shell, -Q-H on the outer surface. Based just on those, what would you determine the field within the body of the shell to be?

 

[assaftolko]

As I said, all the charge is on the surfaces. Suppose the charge on the inner surface is H. So you have 3Q on the central sphere, H on the inner surface of the shell, -Q-H on the outer surface. Based just on those, what would you determine the field within the body of the shell to be?

well since the field inside the boundries of the shell has to be 0, that means that Qin inside a gausien surface with radius R3>r>R2 also has to be 0. all of these surfaces contain the sphere of 3Q and they also contain the inner surface of the shell, so on the inner surface I would expect -3Q, and so - on the outer surface of the shell I would expect 2Q in order to have total of -Q for the whole shell. Correct?

 

[haruspex]

well since the field inside the boundries of the shell has to be 0, that means that Qin inside a gausien surface with radius R3>r>R2 also has to be 0. all of these surfaces contain the sphere of 3Q and they also contain the inner surface of the shell, so on the inner surface I would expect -3Q, and so - on the outer surface of the shell I would expect 2Q in order to have total of -Q for the whole shell. Correct?

Yes indeed.

 

[assaftolko]

thanks!