Consider the concentric metal sphere and spheical shells that are shown in the f
ID: 1572953 • Letter: C
Question
Consider the concentric metal sphere and spheical shells that are shown in the figure below. The innermost is a solid sphere that has a radius R1. A spherical shell surrounds the sphere and has an inner radius R2 and an outer radius R3. The sphere and the shell are both surrounded by a second spherical shell that has an inner radius R4 and an outer radius Rs. None of the three objects initially have a net charge. Then, a negative charge -Qo is placed on the inner sphere and a positive charge +Qo is placed on the outermost shell Rs R4 R3 Ri (a) After the charges have reached equilibrium, what will be the direction of the electric field between the inner sphere and the middle shell? O counter-clockwise clockwise O away from the center O toward the center (b) What will be the charge on the inner surface of the middle shell? (Use the following as necessary: Qo-) (c) What will be the charge on the outer surface of the middle shell? (Use the following as necessary: Qo-) (d) What will be the charge on the inner surface of the outermost shell? (Use the following as necessary: Qo-) (e) What will be the charge on the outer surface of the outermost shell? (Use the following as necessary: Qo-)Explanation / Answer
part a:
using gauss’ law, electric field is dependent upon charge enclosed.
here charge enclosed is -Q0.
hence the field will be towards the center.
part b:
as field inside a conductor is zero, due to static induction, charge on inner surface of middle shell=-(charge on the solid sphere)=-(-Q0)
=Q0
part c:
equal and opposite charge w.r.t. inner shell will appear on outer shell.
total charge on outer shell=-(Q0)
part d:
on inner surface of outermost shell, using gauss’ law, charge will be equal but opposite sign of charge on the outer surface of middle shell.
hence answer is -(-Q0)=Q0
part e:
total charge on the outer shell=Q0
due to charge mirroring, charge on outer surface=-(charge on inner surface of outer shell)=-Q0
then total charge=Q0-Q0=0