Question

Obtain an expression for the work done to dissociate the system of three charges q, −4q and 2q placed at the vertices A, B and C respectively of an equilateral triangle of side ‘a’.

Answer 1

Given charges are q₁ = q, q₂ = −4q, and q₃ = 2q.

The distance between any two charges is r = a.

Electrostatic Potential Energy (U) = `k sum (q_i q_j)/(r_(ij))`

= `k[(q_1 q_2)/a + (q_2 q_3)/a + (q_3 q_1)/a]`

= `k/a[(q) (-4q) + (-4q)(2q) + (2q) (q)]`

= `k/a[-4q^2 - 8q^2 + 2q^2]`

= `k/a[-10q^2]`

= `-(10 kq^2)/a`

The work required to dissociate (separate the charges to infinity) is:

W = 0 − U

= `-(-(10 kq^2)/4)`

= `(10 kq^2)/a`