In this problem, we'll be dealing with electric fields and a conducting sphere.

Gauss law:

$\overline{){{\mathbf{\varphi}}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\oint}}{\mathbf{E}}{\mathbf{\xb7}}{\mathbf{d}}{\mathbf{A}}{\mathbf{=}}\frac{\mathbf{Q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}}$

**(a) **

**(i)** The charge enclosed at the center of the sphere is zero.

A small conducting spherical shell with inner radius a and outer radius *b* is concentric with a larger conducting spherical shell with inner radius c and outer radius *d*. The inner shell has total charge +3q, and the outer shell has charge +5q.

(a) Calculate the magnitude and direction of electric field E in terms of *q* and the distance *r* from the common center of the two shells for

(i) r < a;

(ii) a < r < b;

(iii) b < r < c;

(iv) c < r < d;

(v) r > d.

(b) What is the total charge on the (i) inner surface of the small shell; (ii) outer surface of the small shell; (iii) inner surface of the large shell; (iv) outer surface of the large shell?

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