Torque on a dipole

Advanced

Electric or magnetic dipoles feel torque in fields.

Key relationτ = p×E

An electric dipole p in a field E feels τ = p × E; a magnetic dipole feels τ = m × B. It aligns with the field, like a compass needle.

Worked example

Compass needles align with Earth's field.

Common mistake

Torque is zero when aligned or anti-aligned, but only aligned is stable.

In more detail

A magnetic dipole in a uniform field experiences a torque τ = μ × B that tends to align it with the field. Its energy depends on its orientation.

Compass needles align with Earth's magnetic field because of this torque.
Electric motors use torque on current loops in magnetic fields.
A compass needle, which is a small magnetic dipole, turns to line up with the Earth's magnetic field because of torque.

Does the dipole move?

Not in a uniform field, only rotates towards alignment.

Where is the energy lowest?

When the dipole is aligned with the field.

Why does a dipole turn in a field?

The field exerts forces on the two poles in opposite directions, which produce a torque that aligns the dipole.