Question

Consider a spherical Gaussian surface of radius $r>c$, the net charge enclosed by this surface is $Y\times Q$. Find out the value of $Y$?

Answer 1

As inner solid sphere has charge $+3Q$ so the inner surface of shell will get charge $-3Q$ and the outer surface will get charge $+3Q$ such that total induced charge is zero. So, net charge on outer surface is $+3Q-Q=2Q$

When consider Gaussian surface of radius $r>c$ , the all spheres are inside the Gaussian surface. Thus total charge inside it is $Q_t=3Q-3Q+2Q=2Q$