Question

Figure shows three concentric thin spherical shells A, B, and C of radii $R$, $2R$, and $3R$ respectively. The shell B is earthed and A and C are given charges $q$ and $2q$ respectively. If the charge on surfaces 1, 2, 3, and 4 are $q_1$, $q_2$, $q_3$, and $q_4$ respectively, then match the following columns :

Answer 1

As charge inside shell is zero so charge distribution will be as shown in figure below. Thus charge induced at surface 1 is $q_1=-q$
As shell B is earthed so potential at any point (P) on this shell will be zero.i,e
$V_P=0=V_{A,out}+V_{B,surface}+V_{C,in}$
Lets assume charge on B's surface $q_2$ is $x$
or $0=k\frac{q}{2R}+k\frac{(-q+x)}{2R}+k\frac{2q}{3R}$
or $0=k\frac{x}{2R}+k\frac{2q}{3R}$
$x=-\frac{4}{3}q$
Thus, $q_2=x=-\frac{4}{3}q,q_3=-x=\frac{4}{3}q$ and $q_4=2q+x=2q-\frac{4}{3}q=\frac{2}{3}q$