Question

Two conducting spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$ respectively are placed very far apart from each other. Now they are connected to each other by a connecting wire, then there is

• A. no change in the energy of the system
• B. an increase in the energy of the system
• C. always a decrease in the energy of the system
• D. a decrease in energy of the system unless $q_{1}R_{2} \, = \, q_{2}R_{1}$

Answer 1

Answer: (D)

$\Delta U \, = \, \frac{1}{2} \, \left(\frac{C_{1} C_{2}}{C_{1} + C_{2}}\right) \, \left(V_{1} \, - \, V_{2}\right)^{2}$
$\Delta U \, = \, 0$ , If $V_{1} \, = \, V_{2}$
or $\frac{k q_{1}}{R_{1}} \, = \, \frac{k q_{2}}{R_{2}}$
or $q_{1}R_{2}=q_{2}R_{1}$