HSC Science (General) 11thMaharashtra State Board
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A Conductor a with a Cavity as Shown in Fig. 1.36(A) is Given a Charge Q. Show that the Entire Charge Must Appear on the Outer Surface of the Conductor. - HSC Science (General) 11th - Physics

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Question

(a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor. (b) Another conductor B with charge is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is [Fig. 1.36(b)]. (c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

Solution

Let us consider a Gaussian surface that is lying wholly within a conductor and enclosing the cavity. The electric field intensity E inside the charged conductor is zero.

Let q is the charge inside the conductor and `in_0`is the permittivity of free space.

According to Gauss’s law,

Flux, `phi=vecE.vec(ds)=q/in_0`

Here, = 0

`q/in_0=0`

`in_0ne0`

`therefore q=0`

Therefore, charge inside the conductor is zero.

The entire charge Q appears on the outer surface of the conductor.

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

(c) A sensitive instrument can be shielded from the strong electrostatic field in its environment by enclosing it fully inside a metallic surface. A closed metallic body acts as an electrostatic shield.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 1: Electric Charge and Fields
Q: 28 | Page no. 49

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Solution A Conductor a with a Cavity as Shown in Fig. 1.36(A) is Given a Charge Q. Show that the Entire Charge Must Appear on the Outer Surface of the Conductor. Concept: Continuous Charge Distribution.
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