Question

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

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 $r$ where $b>r>a$. Thus total charge inside it is $Q_{in}=3Q$