Figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$, the inner most shell has charge $q_1$, and the middle shell is uncharged. The charge appearing on the inner surface of outermost shell is

$(a)$ A conductor $A$ with a cavity as shown in Figure $(a)$ is given a charge $Q$. Show that the entire charge must appear on the outer surface of the conductor.

$(b)$ Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A \text { is } Q+q$ [Figure $(b)$]

$(c)\;A$ sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

A hollow conducting sphere of inner radius $R$ and outer radius $2R$ is given a charge $Q$ as shown in the figure, then the :

‘At the surface of a charged conductor electrostatic field must be normal to the surface at every point’. Explain.

A hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in figure. Let ${V_A},{V_B},{V_C}$ be the potentials at points $A,B$ and $C$ respectively. Then

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume in the figure. The electric field inside the emptied space is