$A$ point charge $q$ is placed in a cavity in a metal block. If a charge $Q$ is brought outside the metal,then the electric force experienced by $q$ is

$A$ dipole consisting of two charges $\pm q$ separated by a distance $2a$ is placed with its centre at a distance $D$ from the center of a grounded conducting sphere of radius $R$ $(D \gg a)$. When the dipole moment vector is perpendicular to the line joining the two centres (those of the dipole and sphere),the total charge induced on the sphere 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.

Two metal spheres,one of radius $R$ and the other of radius $2R$,respectively,have the same surface charge density $\sigma$. They are brought in contact and separated. What will be the new surface charge densities on them?

Can there be a potential difference between two adjacent conductors carrying the same charge?

Given below are two statements $:$ one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes.
Reason $(R) :$ The electric field inside the cavity enclosed by a conductor is zero.
In the light of the above statements,choose the most appropriate answer from the options given below.