Question 448: Electrostatics & Capacitance

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 $\overrightarrow P $
 as shown. In this case :
![](https://imagex.cdn.examgoal.net/3rsa0w2w9jx3au204/6144e1d9-d497-4eff-a6f0-f99db6412c6e/e73df640-9299-11e9-86c1-73f7f991b766/file-3rsa0w2w9jx3au205.png)

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 observer outside the shell, the resultant
electric field is due to Q uniformly distributed on outer
surface only and it is equal to.
$E = {{KQ} \over {{r^2}}}$

Answer

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

Answer

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

Answer

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

Answer

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

Electrostatics & Capacitance

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 \overrightarrow P as shown. In this case :

Choose the correct answer: