Question

Three charges ` 0.1` coulomb each are placed on the corners of an equilateral triangle of side `1 m`. If the energy is supplied to this system at the rate of ` 1 kW` how much time would be required to move one to the charges on to the midpoint of the line joining the two ?

Answer 1

Correct Answer - 50 hr.
As potential energy of two point charges separated by a distance r is given by `U = (q_1 q_2 // 4 pi epsilon_0 r)`, the initial and final potential energies of the system will be
`(U s)_1 = 3 xx (1)/(4 pi epsilon_0) (q^2)/( r) = 3 xx 9 xx 10^9 xx (0.1)^2/(1) = 2.7 xx 10^8 J`
`(U s)_F = 2 xx (1)/(4 pi epsilon_0)(q^2)/((r //2)) + (1)/ (4 pi epsilon_0)(q^2)/(r) = 5 xx (q^2)/(4 pi epsilon_0 r) = 4.5 xx 10^8 J`

So work done in changing the configuration of the system
`W = (U s)_F - (Us)_1 = 1.8 xx 10^8 J`
Now, as energy is supplied at the rate of `1 k W`, i.e., `10^3 J s^-1`, time required to do work W is given by
`t = (W)/P = (1.8 xx 10^8)/(10^3) = 1.8 xx 10^5 s = 50 h`.