Q20 / 250 · NTA Abhyas (NEET) 2020 · Physics · Electrostatics

Two insulated charged spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$ respectively are connected to each other; 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
Correct answer
D
a decrease in energy of the system unless $Q_{1} R_{2} = Q_{2} R_{1}$

Solution

Δ U = \frac{1}{2} (\frac{C_{1} C_{2}}{C_{1} + C_{2}}) {(V_{1} - V_{2})}^{2}

Δ U = 0

, If

V_{1} = V_{2}

\frac{k Q_{1}}{R_{1}} = \frac{k Q_{2}}{R_{2}}

Q_{1} R_{2} = Q_{2} R_{1}

Hence, the correct answer is option: 'D'.