A small conducting spherical shell with inner radius a and outer radius b is con

Question

A small conducting spherical shell with inner radius aand outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d(Figure 1) . The inner shell has total charge +2q, and the outer shell has charge ?2q.

Calculate the magnitude of the electric field in terms of q and the distance r from the common center of the two shells for r<a.

Calculate the magnitude of the electric field for a<r<b.

A small conducting spherical shell with inner radius aand outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d(Figure 1) . The inner shell has total charge +2q, and the outer shell has charge ?2q. Calculate the magnitude of the electric field in terms of q and the distance r from the common center of the two shells for r

Explanation / Answer

electric field for r<a

using Gauss Law charge enclosed = 0

so E = 0

electric field for a<r<b

E*4pi*r^2 = integral from a to r 2q/(4pi(b^3-a^3)) *4pir^2dr/epsilon0

==> E = 2q/(4pi(b^3-a^3)*epsilon0) (r-a)

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