Two Multiple Choice Questions from Electrostatics
Let us consider the following questions:
(1) What fraction of the energy drawn from the charging battery is stored ina capacitor?

(a) 100% (b) 50% (c)75% (d) 70.7% (e) 41.4%

With usual notations, the energy of a charged capacitor is ½CV^2 = ½QV. Since the charge Q is flowing under the action of the e.m.f. V of the charging battery, the energy supplied by the battery is QV. Therefore, the fraction of the energy stored is ½QV/QV = ½ = 50%.

(2) A charge ‘q’ is placed at the centre of the line joining two equal point charges, each equal to +Q. This system of three charges will be inequilibrium if q is equal to

(a) +Q (b) +Q/2 (c) –Q/2 (d) +Q/4 (e) –Q/4

+Q____q_____+Q Since the force on the charge ‘q’ placed at the centre will be zero irrespective of the sign of ‘q’, it is enough to set the condition for zero net force on the charge +Q. Therefore, 1/4πε0[Q^2/d^2 + Qq/(d/2)^2] = 0 where ‘d’ is the separation between the charges Q&Q. From this we get q = -Q/4, making (e) the correct option.