$A$ small conducting sphere is hung by an insulating thread between the plates of a parallel plate capacitor as shown in the figure. The net force on the sphere is

$A$ solid conducting sphere of radius $a$ has a net positive charge $2Q$. $A$ conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$. The surface charge density on the inner and outer surfaces of the spherical shell will be

Write important results regarding the electrostatics of conductors.

Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated,the surface charge density on the smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$,respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is:

$A$ charge of $Q$ coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself:

$A$ 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: