Question

an electric dipole experiences maximum torque of 12 Nm in a uniform electric field. what is the minimum potential energy of the dipole in the same field?

Answer 1

Torque = p×​E = PEsin$\theta$
where p is the dipole moment, E is the uniform electric field.
$\theta$ is the angle between P ans E.
FOR maximum torque $\theta$ must be $\pi$/2.
$\tau$ = PE---- (1)

potential energy = -P.E = -PEcos$\theta$
for minimum potential energy $\theta$ must be equal to $\pi$.
U = PE---(2)

from equation (1) and (2) , we get
maximum torque is equal to the minimum potential energy.

Therefore minimum potential energy = 12 joule.