$A$ 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:

Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are placed at a distance of $5\, cm$ from each other. They carry equal charges. If the spheres are connected by a conducting wire,they reach an equilibrium state. The ratio of the magnitudes of the electric fields at the surfaces of spheres $A$ and $B$ 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.

$A$ 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:

$A$ charge $+q$ is placed somewhere inside the cavity of a thick conducting spherical shell of inner radius $R_1$ and outer radius $R_2$. $A$ charge $+Q$ is placed at a distance $r > R_2$ from the centre of the shell. Then the electric field in the hollow cavity

$A$ point charge $Q$ is placed inside a cavity within a solid isolated conducting sphere. Consider points $A$, $B$ and $C$, where the magnitudes of the electric fields are $E_A$, $E_B$ and $E_C$, respectively. The points $B$ and $C$ are at the same distance from the center of the solid sphere. The correct option is: