$(a)$ 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 solid uncharged conducting sphere has radius $3a$ contains a hollowed spherical region of radius $2a$. A point charge $+Q$ is placed at a position a distance a from the common center of the spheres. What is the magnitude of the electric field at the position $r = 4a$ from the center of the spheres as marked in the figure by $P?$ $\left( {k = \frac{1}{{4\pi { \in _0}}}} \right)$

Charges $Q, 2Q$ and $-Q$ are given to three concentric conducting shells $A, B$ and $C$ respectively as shown the ratio of charges on inner and outer surfaces of shell $C$ will be

‘The interior of a conductor can have no excess charge in the static situation’. Explain.

If electric potential of the inner sphere is $10\, volt$ and that of the outer shell is $50\, volt$ then potential at common centre is :-……$V$