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(a) A conductor A with a cavity as shown in Fig. (a) is given a charge must appear on the outer surface of the conductor.
(b) Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A$ is Q $+$ q [Fig. (b)].
(c) A sensitive instrument is to be shielded from the strong electrostatic field in its environment. Suggest a possible way.
(b) Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A$ is Q $+$ q [Fig. (b)].
(c) A sensitive instrument is to be shielded from the strong electrostatic field in its environment. Suggest a possible way.
Solution:
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(a) Taking a close Gaussian surface just inside touching the outer surface of the conductor (A). Since electric field inside the Gaussian surface is zero.
$\therefore \oint \overrightarrow{\mathrm{E}} \mathrm{ds}=\frac{\mathrm{Q}}{\varepsilon_0}=0$
Hence there is no charge inside the Gaussian surface and whole charge Q lies on the outer surface of conductor $\mathrm{A}$.
(b) Charge $+\mathrm{Q}$ appears on conductor $\mathrm{A}$ forming cavity. Induced charge $+q$ appears on outer surface of $\mathrm{A}$. Therefore, total charge $(\mathrm{Q}+q)$ appears on outer surface of $\mathrm{A}$.
(c) The instrument should be enclosed inside a metallic case to make its environment field free.
$\therefore \oint \overrightarrow{\mathrm{E}} \mathrm{ds}=\frac{\mathrm{Q}}{\varepsilon_0}=0$
Hence there is no charge inside the Gaussian surface and whole charge Q lies on the outer surface of conductor $\mathrm{A}$.
(b) Charge $+\mathrm{Q}$ appears on conductor $\mathrm{A}$ forming cavity. Induced charge $+q$ appears on outer surface of $\mathrm{A}$. Therefore, total charge $(\mathrm{Q}+q)$ appears on outer surface of $\mathrm{A}$.
(c) The instrument should be enclosed inside a metallic case to make its environment field free.
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