1.28 (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 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. 1.36(b)].

 

(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

<p><strong>1.28 </strong><strong>(a)</strong> 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.</p><p>Let q be the charge inside the conductor and <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>?</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></math></span>&nbsp;the permittivity of free space.</p><p>According to Gauss’s law, Flux,<span title="Click to copy mathml"><math><mi>φ</mi></math></span> &nbsp;= E.ds = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>q</mi></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>?</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span></p><p>Here, E = 0, hence <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>q</mi></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>?</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub></mrow></mrow></mfrac></math></span>&nbsp;= 0, so q = 0 (as <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>?</mi></mrow></mrow><mrow><mrow><mn>0</mn></mrow></mrow></msub><mo>≠</mo><mn>0</mn><mo>)</mo></math></span></p><p>Therefore, the charge inside the conductor is zero. The entire charge Q appears on the outer surface of the conductor.</p><p>&nbsp;</p><p><strong>(b)</strong> The outer surface of the conductor A has a charge amount Q. Another conductor B, having charge +q is kept inside conductor A and it is insulated from A. Hence, a charge of amount –q will be induced in the inner surface of the conductor A and +q is induced on the outer surface of conductor A. Therefore, total charge on the outer surface of the conductor A is Q+q.</p><p>&nbsp;</p><p><strong>(c)</strong> 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.</p>

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