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 vecp as shown. In this case :

Question

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 vecp as shown. In this case : (A) Electric field outside the shell is the same as that of a point charge at the centre of the shell. (B) Surface charge density on the inner surface of the shell is zero everywhere. (C) Surface charge density on the inner surface is uniform and equal to ((Q /2)/4π a2) (D) Surface charge density on the outer surface depends on | vecp|

Tardigrade Admin · Accepted Answer

Total charge of dipole = 0, so charge induced on outside surface = 0.
But due to non uniform electric field of dipole, the charge induced on inner surface is non zero and non uniform.
So, for any abserver outside the shell, the resultant electric field is due to Q uniformly distributed on outer surface only and it is equal to.

E = \frac{K Q}{r ^{2}}

Q. 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 $p$ as shown. In this case :

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

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 $\frac{( Q /2 )}{4 π a ^{2}}$

Surface charge density on the outer surface depends on $∣ p ∣$

Q. 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 p​ as shown. In this case :

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

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 4πa2(Q/2)​

Surface charge density on the outer surface depends on ∣p​∣

Q. 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 $p$ as shown. In this case :

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

Surface charge density on the outer surface depends on $∣ p ∣$