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Question -

(a) A conductor A with acavity as shown in Fig. 1.36(a) is given a charge Q. Show that theentire charge must appear on the outer surface of the conductor. (b) Anotherconductor B with charge is inserted into the cavity keepingB insulated from A. Show that the total charge on the outside surface of Ais [Fig. 1.36(b)]. (c) A sensitiveinstrument is to be shielded from the strong electrostatic fields in itsenvironment. Suggest a possible way.

                   



Answer -

(a) Let us consider a Gaussiansurface that is lying wholly within a conductor and enclosing the cavity. Theelectric field intensity E inside the charged conductor iszero.

Let q isthe charge inside the conductor and is the permittivity of freespace.

According to Gauss’s law,

Flux, 

Here, =0

Therefore, charge insidethe conductor is zero.

The entire charge Q appearson the outer surface of the conductor.

(b) The outer surface ofconductor A has a charge of amount Q. Another conductor B havingcharge +q is kept inside conductor A and it is insulated from A.Hence, a charge of amount −will be induced in the inner surfaceof conductor A and +q is induced on the outer surface of conductorA. Therefore, total charge on the outer surface of conductor A is Q q.

(c) A sensitive instrument canbe shielded from the strong electrostatic field in its environment by enclosingit fully inside a metallic surface. A closed metallic body acts as anelectrostatic shield.

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