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

A thin metallic spherical shell contains a charge $Q$ on it. A point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in fig. All  the three charges are positive. The force on the central charge due to the shell is :-

Three concentric conducting spherical shells have radius $ r, 2r$ and $3r$ and $Q_1, Q_2$ and $Q_3$ are final charges respectively. Innermost and outermost shells are already earthed as shown in figure. Choose the wrong statement.

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

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q. $

$(a)$ A charge $q$ is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

$(b)$ Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

For a spherical shell