Two conducting spheres of radii `r_(1)` and `r_(2)` having charges `Q_(1)` and `Q_(2)` respectively are connected to each other. There is

Options

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 the energy of the system unless `Q_(1)r_(2)=Q_(2)r_(1)`

Answer

D

Explanation

If potentials of two spheres are same i.e.,
`V_(1)=V_(2)implies(Q_(1))/(4piin_(0)r_(1))=(Q_(2))/(4piin_(0)r_(2))`
`Q_(1)r_(2)=Q_(2)r_(1)`
There will be no redistribution of charge and hence no loss of energy