Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow{E}$,the electric field within the plate

Two conductors of the same shape and size,one of copper and the other of aluminium (which is less conducting),are placed in a uniform electric field. What can be said about the charge induced in the aluminium conductor?

The figure shows a solid conducting sphere of radius $1 \, m$,enclosed by a metallic shell of radius $3 \, m$ such that their centers coincide. If the outer shell is given a charge of $6 \, \mu C$ and the inner sphere is earthed,find the charge on the surface of the inner sphere in $\mu C$.

$A$ solid conducting sphere has a cavity,as shown in the figure. $A$ charge $+q_1$ is situated away from the center. $A$ charge $+q_2$ is situated outside the sphere. Then the true statement is:

Two isolated metallic solid spheres of radii $R$ and $2R$ are charged such that both have the same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$,then the ratio $\frac{\sigma^{\prime}}{\sigma}$ 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 $A$ 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.