Shown in the figure are two point charges + Q and - Q inside the cavity of a spherical shell. The charges…

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 ${\sigma }_1$ is the surface charge on the inner surface and $Q_1$ net charge on it and ${\sigma }_2$ the surface charge on the outer surface and $Q_2$ net charge on it then:

1. ${\sigma }_1=0, Q_1=0$ , ${\sigma }_2=0, Q_2=0$
2. ${\sigma }_1\ne 0, Q_1=0$ , ${\sigma }_2\ne 0, Q_2=0$
3. ${\sigma }_1\ne 0,Q_1\ne 0$ , ${\sigma }_2\ne 0, Q_2\ne 0$
4. ${\sigma }_1\ne 0, Q_1=0$ , ${\sigma }_2=0, Q_2=0$

Solution

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 the Gaussian surface$=0$,$\Rightarrow$ The 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, ${\sigma }_1=0$

$\because Q_1=0$ on the inner surface

So, net charge $Q_2=0$ on the outer surface as conductor is neutral but $\because$ outer surface is free from any electric field so no charge density exists on the outer surface. So, ${\sigma }_2=0$ .

Asked in: JEE Main 2015 (10 Apr Online)

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