A solid spherical conducting shell has inner radius a and outer radius $2a$. At the center of the shell is located a point charge $+Q$. What must the excess charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal ?

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 equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is

Two isolated metallic solid spheres of radii $R$ and $2 R$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$. The ratio $\frac{\sigma^{\prime}}{\sigma}$ is

The dielectric strength of air at $NTP$ is $3 \times {10^6}\,V/m$ then the maximum charge that can be given to a spherical conductor of radius $3\, m$ is

Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an electrostatic field $\overrightarrow E $, the electric field within the plate

The vehicles carrying inflammable fluids usually have metallic chains touching the ground: