# Will the torque tend to rotate a dipole in a uniform external field if it is in unstable equilibrium?

A dipole of length $l$ will experience a net torque of magnitude $pE\sin\theta$ when placed in a uniform external electric field and there will be no net force (since the field is uniform).

Also, the torque will tend to align the dipole with the field and bring it to a stable equilibrium.

My question is, if the dipole is in unstable equilibrium, i.e. the angle between $p$ (dipole moment) and the field is 180°, will the torque still tend to align it will the field or not?

• Its higly likely. Even the slightest of disturbance would cause it to lose its state of equilibrium. The potential energy function is at a maxima at that $\theta$. Moreover, $\frac{d^2 U}{d\theta^2} < 0$. And as F = $-\frac{dU}{d\theta}$, it is evident that around equlibrium $\theta$, for small disturbances, force goes on increasing. – SJ. Mar 13 '17 at 8:09
• Why would this be any different to every other situation with unstable equilibrium? – Emilio Pisanty Mar 13 '17 at 9:09

If the angle between the field and the dipole moment vector is maintained at $180^0$,the field cannot align the dipole. The field has to exert a torque on the dipole to rotate it and align it along the field direction. Torque can be exerted only if the field can exert a force. But in the position mentioned the field exerts no force on the dipole. But if the dipole is slightly displaced from its unstable equilibrium position, then the field aligns the dipole along the field direction.