A dipole is formed by two point charge -q and +q, each of mass m, and both the point charge are connected by a rod of length `l` and mass m. This dipole is placed in uniform electric field `vec(E)` If the dipole is disturbed by a small angle `theta` from stable equilibrium position, prove that its motion will be almost SHM. also find its time period.

Explanation

If the dipole is disturbed by `theta` angle, `tau_("net")=-PE sin theta` (Here -ve sign indicates that direction `theta` torque is opposite to `theta`)

If `theta` is very small, `sin theta ~~ theta`
`:. Tau_("net")=-(PE) theta`
`tau_("net") prop (-theta)` so motion will be almost SHM & C = PE (where, `P=ql`)
`:' T=2pi sqrt(I/C)`
`:. T=2m^(-) sqrt(((ml)/12+2m (l/2)^(2))/(P.E))=2pi sqrt(((ml)/12+(ml^(2))/2)/(qlE))=2pi sqrt((7ml^(2))/(12 q lE))=2pi sqrt((7 ml)/(12 qE))`
`T=pi sqrt((7 ml)/(3qE))`