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 `4 sqrt(3) N m`. Calculate the
a. magnitude of the electric field, and
b. potential energy of the dipole, if the dipole has charges of `+- 8 n C`.

Explanation

Here, `q = +- 8 xx 10^-9 C , 2 a = 4 cm = 0.04 m , tau = 4 sqrt(3) Nm`, and `theta = 60^(@)`
a. Now, `p = q (2 a) = 8 xx 10^-9 xx 0.04 = 3.2 xx 10^-10 Cm`
Torque on the electric dipole is `tau = p E sin theta`
or `E = (tau)/(p sin theta)= (4 sqrt (3))/(3.2 xx 10^-10 xx sin 60^(@))`
=`(4 sqrt(3) xx 2)/(3.2 xx 10^-10 xx sqrt(3))= 2.5 xx 10^10 NC^-1`
b. Potential energy of the electric dipole is
`U = - pE cos theta`
=`-3.2 xx 10^-10 xx 2.5 xx 10^10 xx cos 60^(@)`
=`-3.2 xx 2.5 xx 0.5 = -4 J`.