Potential Energy of an Electric Dipole
An electric dipole of length 4 cm, when placed with its axis making an angle of `60^(@)` with a uniform electric field, experiences a torque of `4sqrt(3)` N-m. Calculate the potential energy of the dipole, if it has charge `pm8nC`.

Explanation

Given, length `2a=4" cm"=4xx10^(-2)m`
Angle, `theta=60^(@)`, torque `tau=4sqrt(3)` N-m
charge, `Q=8nC=8xx10^(-9)C`
We know that, `tau=Q(2a)E sin theta`
`rArr` Electric field,
`E=(tau)/(Q(2a)sin theta)=(4sqrt(3))/(8xx10^(-9)xx4xx10^(-2)xxsin60^(@))" N/C"`
`:.` Potential energy,
`U=-pEcos theta=-Q(2a)Ecostheta`
`=-8xx10^(-9)xx4xx10^(-2)xx[(4sqrt(3)xxcos60^(@))/(8xx10^(-9)xx4xx10^(-2)xx sin 60^(@))]`
`=(-4sqrt(3))/(sqrt(3))J=-4J`