Question

A conducting sphere of radius R carrying charge +Q is connected to an uncharged conducting sphere of radius 2R. The charge that flows between them is

• A. $Q/2$
• B. $Q/3$
• C. $Q/4$
• D. $2Q/3$

Answer 1

Answer: (D)

Charge will not flow if both the sphere get the same potential i.e.
$V_1=V_2$ or, $\frac{Q_1}{C_1}=\frac{Q_2}{C_2}$
Here, $C_1=4\pi {\epsilon }_{0}R,C_2=4\pi {\epsilon }_0\left(2R\right)$
$Q_1+Q_2=Q$
$\therefore \frac{Q_1}{4\pi {\in }_{0}R}=\frac{Q_2}{4\pi {\in }_0\left(2R\right)}or,Q_1=\frac{Q_2}{2}$
From equation (i),
$\frac{Q_2}{2}+Q_2=Qor\frac{3}{2}{Q}_2=Q$
or , $Q_2=\frac{2}{3}Q$
And $Q_1=\frac{1}{3}Q$
Flow of charge $=Q-Q_1=Q_2=\frac{2}{3}Q$