Question

Two conducting spheres, each given a charge $q$ are kept far apart as shown. The amount of charge that crosses the switch $S_1$, where it is closed, is (the connection between the spheres is conducting)

• A. $\frac{q}{3}$
• B. $\frac{2q}{3}$
• C. $\frac{3q}{4}$
• D. $Zero$

Answer 1

The correct option is A $\frac{q}{3}$

Both the conducting spheres are connected by same wire so they have the same potential. Let $x$ is the charge that crosses from smaller sphere to bigger sphere when switch 1 is closed. Then x amount of charge is subtracted from the total charge in the small sphere and x amount of charge is added in the bigger sphere.

$\frac{k(q-x)}{R}=\frac{k(q+x)}{2R}$

$2q-2x=q+x$

$q=3x$

$x=\frac{q}{3}$

$\frac{q}{3}$ amount of charge crosses from smaller sphere to bigger sphere.