Question

Two particles, carrying charges −q and +q and and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.

Answer 1

Consider the rod to be a simple pendulum
Time period of a simple pendulum,
$T=2\mathrm{\pi }\sqrt{\frac{l}{a\text{'}}}$
(where l = length and a' = acceleration)
Now, $a\text{'}=\frac{F}{m}=\frac{Eq}{m}$
and length l = a
∴ The time period,
$T=2\mathrm{\pi }\sqrt{\frac{ma}{qE}}$