Question

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 sytem
• 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)

a decrease in energy of the system unless $q_1{R}_2=q_2{R}_1$

Two insulated charged spheres of radii $R_1,R_2$having charges $q_1,q_2$respectively are brought in contact with each other.

Charges will flow across the point of contact from where they are connected until their potential at their surfaces became same.

Energy is decreased because system changes to get stability.

Potential at their surfaces are same,
So,

$V_1=V_2$

$\frac{K{q}_1}{R_1}=\frac{K{q}_2}{R_2}$

$q_1{R}_2=q_2{R}_1$

Hence Proved.