$A$ solid spherical conducting shell has inner radius $a$ and outer radius $2a$. At the center of the shell, a point charge $+Q$ is located. What must the charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal?

$A$ 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:

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

$A$ and $B$ are two concentric conducting spherical shells. $A$ is given a positive charge $+Q$ while $B$ is earthed. Then:

Which of the following statements is $NOT$ true for a charged conducting sphere?

$A$ point charge of magnitude $+ 1\,\mu C$ is fixed at $(0, 0, 0)$. An isolated uncharged spherical conductor is fixed with its center at $(4, 0, 0)$. The potential and the induced electric field at the center of the sphere are: