Shown in the figure are two point charges + Q and - Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ 1 i

Question

Shown in the figure are two point charges $+ Q$ and $- Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If $σ_{1}$ is the surface charge on the inner surface and $Q_{1}$ net charge on it and $σ_{2}$ the surface charge on the outer surface and $Q_{2}$ net charge on it then:

TestHub · Accepted Answer

By the property of electrostatic shielding in the conductors $E = 0$ in the conductor.

So electric flux = 0 through a dotted Gaussian surface as shown

The net enclosed charge through Gaussian surface = 0

$\Rightarrow$ Net charge $Q_{1}$ on the inner surface = 0 but the equal and opposite induced charge on the surface will be distributed non uniformly on the inner surface

So, $σ_{1} = 0$

$∵ Q_{1} = 0$ on the inner surface

So, net charge $Q_{2} = 0$ on the outer surface as conductor is neutral but $∵$ outer surface is free from any electric field so no charge density exists on the outer surface. So, $σ_{2} = 0$ .

Physics - Electrostatics Question with Solution | TestHub

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