Question

Question 2.15: 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.

Class 12 - Physics - Electrostatic Potential And Capacitance Electrostatic Potential And Capacitance Page-88

Answer 1

We know, charge have nature to reside on outer surface od conductor . Now if a charge q is placed at the centre of the shell, -q charge induced imner surface of conducting shell .
so, surface charge density on the inner surface of the shell is
$\sigma=\frac{-q}{4\pi r_1^2}$

Charge on outer surface of shell is (Q + q)
So, surface charge density on the outer surface of shell is
$\sigma_{out}=\frac{Q+q}{4\pi r_2^2}$


(b) the electric flux linked with any closed surface inside the conductor is zero as electric field inside the conductor is zero.
So, by Gaussian theorem, net charge enclosed by closed surface is also zero.
e.g., $q_{net}=0$
So, there is no charge inside the cavity, then there cannot be any charge on the inner surface of the shell and hence electric field inside the cavity will be zero , even through the shell may not be spherical.

Answer 2

Answer:

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