Two charges – q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid – point is displaced slightly by x…

Q: Two charges – q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid – point is displaced slightly by x(x << d)perpendicular to the line joining the two fixed charged as shown in figure. show that q will perform simple harmonic oscillation of time period.

$\large T = \frac{8 \pi^3 \epsilon_0 m d^3 }{q^2}$

Numerical