Electric Fields with Calculus Video Lessons

Concept

Problem: 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 &lt; a;(ii) a &lt; r &lt; b;(iii) b &lt; r &lt; c;(iv) c &lt; r &lt; d;(v) r &gt; 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?

FREE Expert Solution

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

Gauss law:

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

(a)

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

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Problem Details

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?