Two spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is:
$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non-uniformly distributed on $A$

$A$ 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

Two thin conducting concentric shells of radii $R$ and $2R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. When the switch $K$ is closed,which of the following statement$(s)$ is/are correct?
$(a)$ The potential on the inner shell becomes zero.
$(b)$ The charge on the inner shell is $\frac{Q}{2}$.

$A$ hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in the figure. Let $V_A, V_B$,and $V_C$ be the potentials at points $A, B$,and $C$ respectively,where $A$ and $B$ are on the surface of the sphere and $C$ is inside the sphere. Then:

Some charge is being given to a conductor. Then its potential is

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2r$. $A$ point charge $+Q$ is now placed inside the shell at a distance $r/2$ from the centre. The shell is then grounded by connecting the outer surface to the earth. $P$ is an external point at a distance $2r$ from the point charge $+Q$ on the line passing through the centre and the point charge $+Q$ as shown in the figure. The magnitude of the force on a test charge $+q$ placed at $P$ will be