Torque on a dipole in a field

Intermediate

A dipole rotates to align with the field.

Key relationτ = pE sinθ

A dipole in a uniform field feels torque τ = p × E, magnitude pE sinθ, rotating it to align with E. There's no net force in a uniform field.

Worked example

p = 10⁻²⁹ C·m in 10⁵ N/C at 90°: 10⁻²⁴ N·m.

Common mistake

In a non-uniform field there's also a net force.

In more detail

A dipole in a uniform electric field experiences a torque τ = pE sin θ, which tends to align it with the field.

Microwave ovens heat food by rotating water dipoles in an oscillating field.
Liquid crystal displays use torques on dipoles to switch pixels.
A polar molecule in a microwave oven rotates to align with the oscillating electric field, heating the food.

What is the equilibrium orientation?

Aligned with the field, where the torque is zero and the energy is lowest.

Does a uniform field push the dipole?

No net force acts, only a torque, since the field is the same at both charges.

Why do microwaves heat water?

The water molecules are dipoles, so they keep turning to follow the field, which converts energy into heat.