A small charged ball lies within the hollow of a metallic spherical shell of radius R . For three situations, the net charges on the ball and shell, respectively, are

(1)$\mathbf{+}\mathbf{4}\mathit{q}\mathbf{,}\mathbf{0}$;

(2)$\mathbf{-}\mathbf{6}\mathit{q}\mathbf{,}\mathbf{+}\mathbf{10}\mathit{q}$;

(3)$\mathbf{+}\mathbf{16}\mathit{q}\mathbf{,}\mathbf{-}\mathbf{12}\mathit{q}$. Rank the situations according to the charge on

(a) the inner surface of the shell and

(b) the outer surface, most positive first.

A charge ball lies within a hollow metallic sphere of radius R.

The net charges of the ball and the shell for three situations are$+4q,0$,$-6q,+10q$ , and $+16q,-12q$.

Being a conductor, the charge at the surface of the shell is zero. Thus, using this concept, to can get the net charge of the inner and outer surfaces of the shell, and equating it to the charge on the ball; you calculate all the negative and positive charges.

Hence, the rank of the situations according to inner charges of the shell is $2>1>3$.

For, situation 1, induced charge on the inner surface of shell is$-4q$ due to$+4q$at the center.

Net charge on the ball can be given as:

$\begin{array}{l}{Q}_{Net}=0\\ Q_{inner}+Q_{outer}=0\\ -4q+Q_{outer}=0\\ Q_{outer}=+4q\end{array}$

For situation 2, induced charge on the inner surface of shell is $+6q$due to $-6q$at the center.

Net charge on the ball can be given as:

$\begin{array}{l}{Q}_{Net}=+10q\\ Q_{inner}+Q_{outer}=+10q\\ +6q+Q_{outer}=+10q\\ Q_{outer}=+4q\end{array}$

For situation 3, induced charge on the inner surface of shell is $-16q$due to$+16q$ at the center.

Net charge on the ball can be given as:

$\begin{array}{l}{Q}_{Net}=-12q\\ Q_{inner}+Q_{outer}=-12q\\ -16q+Q_{outer}=-12q\\ Q_{outer}=+4q\end{array}$

Hence, the rank of the situations according to the outer charge surface is $1=2=3$.