question_answer 15)

A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q. (a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell? (b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.  

Answer:

(a) Charge Q appears on the outer surface.                 When charge q is placed at the centre, it induces ?q charge on the inner surface and + q on the outer surface.                  charge density of the inner surface,                                 and charge density of the outer surface,                                 (b) Consider a cavity of irregular shape with net charge to be zero inside it. Let a closed loop be partially inside and the rest outside the cavity. The field inside the conductor is zero, so some work is done by the field to carry a test charge in the closed loop, but this is against the provisions of an electrostatic field because as per Gauss' law, the net charge inside a Gaussian surface must be zero. Thus, there cannot be field lines inside the cavity irrespective of its shape.