An electric dipole of length 1 cm which placed with its Axis making an angle of 60 degree with uniform electric field experiences the torque of 6 root 3 Newton metre calculate the potential energy of the dipole if it has a charge of 2 Nano coulomb

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Solution

Dear Student,
As we know the torque on a dipole placed in uniform electric field is given by,
ζ = p X E = pE sinθ = pEsin60^o = $\sqrt{3} / 2 p E$ [given in the ques, angle = 60^o]
the value of tourque is given in ques, ζ = $6 \sqrt{3}$ Nm
so we get, pE = 12 ................(1)

Now we know potential energy of dipole, U = - p . E =- pE cosθ = -pE cos60^o= - pE / 2 ..................(2)
Putting the value of 'pE' from eqn (1) to eqn (2) we get,
U = - 12 / 2
U = - 6 J

Regards.

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