Magnetic Forces and Dipoles

Magnetic fields exert forces on moving charges and currents, and torques that align magnetic dipoles.

Definition

The magnetic force is the velocity-dependent part of the Lorentz force acting on moving charges and currents; a magnetic dipole, characterized by its dipole moment, experiences a torque tending to align it with the field and a force in a non-uniform field.

Scope

This topic covers the magnetic part of the Lorentz force on moving charges, the force and torque on current-carrying conductors, the magnetic dipole moment and its energy, force, and torque in a field, and the field produced by a dipole. It includes why the magnetic force does no work and the dipole approximation for distant current loops.

Core questions

• How does a magnetic field deflect moving charges and current-carrying wires?
• Why does the magnetic force do no work on a point charge?
• How do magnetic dipoles respond to uniform and non-uniform fields?

Key concepts

• Lorentz force
• cyclotron motion
• force on a current
• magnetic dipole moment
• torque on a dipole
• dipole field

Key theories

Lorentz force (magnetic part)

A charge moving in a magnetic field feels a force perpendicular to both its velocity and the field, causing circular or helical motion; because it is always perpendicular to velocity, the magnetic force does no work.

Magnetic dipole in a field

A current loop behaves as a magnetic dipole that experiences a torque aligning it with the field and, in a non-uniform field, a net force; its distant field has the universal dipole form.

Clinical relevance

Magnetic forces drive electric motors, mass spectrometers, cyclotrons, and Hall-effect sensors, while magnetic dipole interactions underlie compass behaviour, magnetic resonance, and the alignment of magnetic materials.

History

Ampère described forces between currents in the 1820s and modelled magnetism as arising from circulating currents. The velocity-dependent force on charges was clarified by Lorentz around 1900, completing the classical picture later named the Lorentz force.

Key figures

• Hendrik Lorentz
• André-Marie Ampère
• Michael Faraday

Seminal works

• jackson1998
• griffiths2017

Frequently asked questions

Why does the magnetic force do no work?

The magnetic force on a charge is always perpendicular to its velocity, so it changes the direction of motion but not the speed, and therefore transfers no energy to the charge.

What is a magnetic dipole moment?

It is a vector characterizing a small current loop or magnet, equal to current times loop area for a loop; it sets the torque the object feels in a field and the strength of the dipole field it produces.