$A$ 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:

Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If $\sigma_1$ is the surface charge density on the inner surface and $Q_1$ is the net charge on it,and $\sigma_2$ is the surface charge density on the outer surface and $Q_2$ is the net charge on it,then:

Two charged spherical conductors of radii $R_1$ and $R_2$ are connected by a wire. The ratio of surface charge densities of the spheres $\sigma_1/\sigma_2$ will be

The metal plate on the left in the figure carries a charge of $+q$. The metal plate on the right has a charge of $-2q$. What charge will flow through the switch $S$ when it is closed,if the central plate is initially neutral?

$A$ spherical conductor of radius $2 \, m$ is charged to a potential of $120 \, V$. It is now placed inside another hollow spherical conductor of radius $6 \, m$. Calculate the potential to which the bigger sphere would be raised. (in $, V$)

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.