Question

Four identical point masses, each of mass m and carrying charge +q are placed at the corners of a square of sides 'a' on a frictionless plain surface. If the particles are released simultaneously, the kinetic energy of the system when they are infinitely far apart is

• A. $\frac{q^2}{4\pi {ϵ}_{0}a}(2\sqrt{2}+1)$
• B. $\frac{q^2}{4\pi {ϵ}_{0}a}(\sqrt{2}+2)$
• C. $\frac{q^2}{4\pi {ϵ}_{0}a}(\sqrt{2}+4)$
• D. $\frac{q^2}{4\pi {ϵ}_{0}a}(\sqrt{2}+1)$

Answer 1

The correct option is C $\frac{q^2}{4\pi {ϵ}_{0}a}(\sqrt{2}+4)$

Neglecting gravitational energy

Initial total electrostatic energy = $\frac{q^2}{4\pi {ϵ}_{0}a}\times 4+\frac{q^2\times 2}{4\pi {ϵ}_{0}a\sqrt{2}}=\frac{q^2}{4\pi {ϵ}_{0}a}[4+\sqrt{2}]$
At infinity $U_{\infty }=0\therefore \Delta U=K.E\Rightarrow K.E=\frac{q^2}{4\pi {ϵ}_{0}a}[4+\sqrt{2}]$