An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$
If another point charge $q_B$ is also placed at a distance $c ( > b) $ the center of shell, then choose the correct statements
force experienced by charge $A$ is $\frac{{\sigma {q_A}{b^2}}}{{{\varepsilon _0}{c^2}}}$
force experienced by charge $A$ is zero
The force experienced by charge $B$ is $\frac{{\sigma {q_B}{b^2}}}{{{\varepsilon _0}{c^2}}}$
The force experienced by charge $B$ is $\frac{{k{q_A}{q_B}}}{{{c^2}}}$
Assertion : A metallic shield in form of a hollow shell may be built to block an electric field.
Reason : In a hollow spherical shield, the electric field inside it is zero at every point.
$(a)$ 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.
Two metallic spheres of radii $1\,cm$ and $2\,cm$ are given charges ${10^{ - 2}}\,C$ and $5 \times {10^{ - 2}}\,C$ respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is
Sixty four conducting drops each of radius $0.02 m$ and each carrying a charge of $5 \,\mu C$ are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be ............
A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge $Q$ is placed at the centre of the spherical cavity. What will be surface charge density on the inner surface