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 a dipole $$\vec{p}$$ is placed as shown then:

Given:
Conducting spherical shell (inner radius a, outer radius b) carrying total charge Q.
$$An\ electric\ dipole\ P\ is\ placed\ at\ the\ centre$$

Concept Used:

• In electrostatic equilibrium, electric field inside the conducting material is zero.
• Induced charges appear on the inner surface to cancel internal fields.
• Net charge on conductor remains conserved.

Analysis:

• The dipole induces charges on the inner surface, but since a dipole has no net charge,

  Total induced charge on inner surface=0

• The conductor already has total charge Q, so:

  Charge on outer surface=Q

Conclusion:

• Inner surface: net charge = 0 (only redistribution due to dipole)
• Outer surface: net charge = Q (uniformly distributed)
• For any external point, the field is same as that due to a charge Q placed at the centre.

Final Answer:

Outer surface charge =Q, Inner surface net charge =0

So for any observer outside the shell, the resultant electric field is due to Q uniformly distributed on the outer surface only