# Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q, At its centre is a dipole $\vec{p}$ as shown. In  this case : Option 1) surface charge density on the outer surface depends on $\left|\vec{p} \right |$ Option 2) electric field outside the shell is the same as that of a point charge at the centre of the shell Option 3) surface charge density on the inner surface is uniform and equal to $\frac{(Q/2)}{4\pi a^{2}}$ Option 4) surface charge density on the inner surface of the shell is zero everywhere

The electric field formed by dipole is non-uniform and hence the charge induced on the inner surface is also non-zero and non-uniform. So far any observed outside the shell, the resultant electric field is due to Q uniformly distributed on outer surface and it is equal to $E=\frac{KQ}{r^{2}}$

Option 1)

surface charge density on the outer surface depends on $\left|\vec{p} \right |$

Option 2)

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

Option 3)

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

Option 4)

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

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