Two spherical conductors A and B of radii a and b (b > o) are placed con-centrically in air as shown in fig. B is given a charge + Q and A is earthed. The equivalent capacitance of the system is

 

detailed solution

Correct option is D

The charge Q given to outer sphere is distributed as e outside and Q2 inside. The inside charge Q2 induces a charge - Q2 on outside of inner sphere and + Q2 on insideof inner sphere which is earthed. The inside of outer sphere and outside of inner sphere constitute a spherical condenser having capacitance 4πε0{ab/(b−a)} andthe outside of the outer constitutes an isolated sphere of capacitance 4πε0b.Now the effective capacitance C is given byC=4πε0ab(b−a)+4πε0b=4πε0ba(b−a)+1=4πε0ba+b−a(b−a)=4πε0b2(b−a)