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

Question

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 a total charge of -1q and the outer shell has a total charge of +3q. Select True or False for the following statements. The total charge on the inner surface of the large shell is +1q The radial component of the electric field in the region r > d is given by +4q/(4n epsilon_0 r^2). The total charge on the outer surface of the large shell is +3q. The total charge on the inner surface of the small shell is -5q. The radial component of the electric field in the region c

Explanation / Answer

Solution - The inner surface of the small shell has no charge. Conductors only have distribution of charges on the surface not inside. Therefore, for r < a, Electric field is zero.

The outer surface of small shell has a charge of -1q because all charges are on the surface where r = b

The inner surface of the large shell is given by

qenclosed = qinner small shell + q outer small shell + qinner large shell

0 = 0 + (-1q) + qinner large shell

therefore, qinner large shell = +1q

The total charge on the outer surface of large shell is given as

+4q = +1q + q(outer large)

q(outer large) = +3q

Only two regions have non-zero electric fields, region (b < r < c) and region (r > d) which is given by -1q/4*pi*e*r2

and 3q/4*pi*e*r2 , respectively

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