Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}$ $(r_{2} > r_{1})$. If the outer shell has a charge $q$ and the inner one is grounded, the charge on the inner shell is

$A$ neutral conducting solid sphere of radius $R$ has two spherical cavities of radius $a$ and $b$ as shown in the figure. The centre-to-centre distance between the two cavities is $c$. Charges $q_a$ and $q_b$ are placed at the centres of the cavities, respectively. The force between $q_a$ and $q_b$ is:

Charge on the outer sphere is $q$ and the inner sphere is grounded. The charge on the inner sphere is $q'$,for $(r_2 > r_1)$. Then

Two thin conducting concentric shells of radii $R$ and $2R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. When the switch $K$ is closed,which of the following statement$(s)$ is/are correct?
$(a)$ The potential on the inner shell becomes zero.
$(b)$ The charge on the inner shell is $\frac{Q}{2}$.

The metal plate on the left in the figure carries a charge of $+q$. The metal plate on the right has a charge of $-2q$. What charge will flow through the switch $S$ when it is closed,if the central plate is initially neutral?

$A$ conducting sphere of radius $10 \ cm$ is charged with $10 \ \mu C$. Another uncharged sphere of radius $20 \ cm$ is brought into contact with it and then separated. The ratio of the surface charge densities on the spheres will be ....... (in $: 1$)