The radii of two metallic spheres $A$ and $B$ are ${r_1}$ and ${r_2}$ respectively $({r_1} > {r_2})$. They are connected by a thin wire and the system is given a certain charge. The charge will be greater:

$(a)$ $A$ 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 $A$ 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.

$A$ metallic sphere $A$ isolated from the ground is charged to $+50 \mu C$. This sphere is brought into contact with another isolated metallic sphere $B$ of half the radius of sphere $A$. Then the charge on the two isolated spheres $A$ and $B$ are in the ratio:

The intensity of the electric field at a charged point inside a hollow metallic container is ....... .

Write important results regarding the electrostatics of conductors.

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