A solid conducting sphere carrying charge q has radius a . It is inside a concen

Question

A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net charge.  Take V = 0 as r??. Use the electric field for this system:  E(r)=???????????0forr?akq/r2fora<r<b0forb<r<ckq/r2forr>c       to calculate the potential V at the following values of r.

Part A) r = c (at the surface of the solid sphere).

Part B) r= b (at the inner surface of the hollow sphere).

Part C) r = a (at the surface of the solid sphere).

Part D) r = 0 (at the center of the solid sphere).

I may be overthinking this problem, but i literally have not even the slightest clue as to how to begin this problem.

Explanation / Answer

here some information you need to know.

1) inside metal the electric field must be zero.

2) any charge material will induce opposite charge to the nearby metal surface.

here the inner sphere will induce same and opposite charge to the inner surface of the hollow sphere. so

a) the electric field st the outer surface of the hollow sphere is zero.(as the charge in the solid and the induced inner surface charge will cancel each other)

b)at the inner of the hollow sphere sees a charge of q due the solid sphere so

E = 1/(4*pi*e)*(q/b^2) V/m

c) at the surface of the solid sphere sees the same q charge.

so E = 1/(4*pi*e)*(q/a^2) V/m (observe the change in radius or distance)

d)

here as we have stated above at r = 0 inside metal field is zero.

so E = 0 V/m

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