A small conducting spherical shell with inner radius a and outer radius b is con
ID: 1592710 • Letter: A
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 -2q and the outer shell has a total charge of +3q.
Select True or False for the following statements.
1)The electric field in the region r < a is zero. 2) The total charge on the inner surface of the large shell is +2q. 3) The total charge on the outer surface of the small shell is -2q. 4)The total charge on the inner surface of the small shell is zero. 5) The electric field in the region r > d is zero. 6)The total charge on the outer surface of the large shell is +1q. 7)The radial component of the electric field in the region c < r < d is given by -2q/(40r2).
Explanation / Answer
There is no charge on the inside surface of the inner shell (a), otherwise there would be an electrical field in the body of the inner shell (a-b), causing current = displacement of charge.
The charge (-2q) is contained in the inner shell outer surface (b).
The inner surface of the outer shell (c) exactly cancels the charge within the sphere (0-c) so that there is not electric field within the shell body (c-d) => its charge is (+1q).
The outer surface of the outer shell (d) has its charge given by the outer shell (c-d) total charge ((+4q)-(+2q)=(+2q)), the same as the total charge of the entire system.
Just remember there is no electric field within a conducting body, and if there's no charge in its interior, there is no field either.