Chapter 22, Problem 22.46P

Repeat Problem 22.45, but now let the outer shell have charge −2q. The inner shell still has charge +2q.

22.45    Concentric Spherical Shells. 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 (Fig. P22.45). The inner shell has total charge +2q, and the outer shell has charge +4q. (a) Calculate the electric field $\stackrel{\to }{\text{E}}$ (magnitude and direction) 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. Graph the radial component of $\stackrel{\to }{\text{E}}$ as a function of r. (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?

Figure P22.45