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 -2q and the outer shell has a total charge of +4q.

Select True or False for the following statements.
The total charge on the inner surface of the large shell is -6q.
The total charge on the inner surface of the small shell is zero.
The electric field in the region c < r < d is zero.
The electric field in the region r > d is zero.
The total charge on the outer surface of the large shell is +2q.
The total charge on the outer surface of the small shell is -6q.
The electric field in the region r < a is zero.

Explanation / Answer

field inside conductor is always zero.

and from Gauss Law,

E. A =Qin / e0

E = 0 hence Qin = 0

for c < r < d

Qin = Q_inner_shell + Qc = 0

-2q + Qc = 0

Qc = 2q .....charge on inner surafce of large shell

for a < r < b

Qin = Qa = 0 ...inner surface of small shell

Qa + Qb = -2q

Qb = -2q ....charge on outer surface of small shell

Qc + Qd = 4q

Qd = 4q - 2q = 2q ..charge on outer surfdace of large shell

E = zero { r < a , a < r < b , c < r < d }

Ans: F T T F T F T

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