A shell made of a conductor has inner radius a and outer radius b. and it carries charge Q. A dipole of dipole moment $\overrightarrow{P}$ is placed at its centre. Choose the correct alternative:

electric field outside the shell is the same as that of a point charge Q at the centre of the shell.

surface charge density on the outer surface depends on $\left|\overrightarrow{\mathrm{P}}\right|$.

surface charge density on the inner surface of the shell is zero everywhere

surface charge density on the inner surface is uniform and equal to $\frac{\left(\frac{\mathrm{Q}}{2}\right)}{4{\mathrm{\pi a}}^2}$