Two spherical conductors $A$ and $B$ of radii $1 \ mm$ and $2 \ mm$ are separated by a distance of $5 \ cm$ and are uniformly charged. If the spheres are connected by a conducting wire,then in the equilibrium condition,the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is:

Explain the electrostatics of conductors. Explain the effects produced inside a metallic conductor placed in an external electric field.

$(a)$ $A$ 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.

$A$ positive point charge $q$ is placed at a distance $2R$ from the surface of a metallic shell of radius $R$. The electric field at the centre of the shell due to the induced charge has a magnitude of:

$A$ and $B$ are two concentric conducting spherical shells. $A$ is given a positive charge $+Q$ while $B$ is earthed. Then:

$A$ metal cube is given a positive charge $(+Q)$. Which of the following statements is true?