Question

Figure shows a solid conducting sphere of radius 1m.
enclosed by a metallic shell of radius 3 m such that
their centres coincide If outer shell is given a charge
of 6 uC and inner sphere is earthed, find magnitude
charge on the surface of inner shell
​

Answer 1

solid conducting sphere (inner sphere) is earthed. it means potential at the surface of inner sphere becomes zero.

Let charge on inner sphere is Q.

now, potential at the surface of inner sphere = potential due to outer sphere + potential due to inner sphere

0 = $\frac{K(6\mu C)}{R}+\frac{KQ}{r}$

or, $\frac{6\mu C}{R}=-\frac{Q}{r}$

putting R = 3m and r = 1m

so, $\frac{6\mu C}{3}=-\frac{Q}{1}$

or, Q = -2$\mu$C

hence, magnitude of charge on the surface of inner sphere = 2$\mu$C