dipoles with the same dipole moment are affected the same way.

Applying the Lorentz force to a (sufficiently small) current loop of arbitrary shape produces a torque on the magnetic dipole of:and a force on the magnetic dipole ofwhere represents the gradient. This force tends to push the magnetic dipole into the direction of increasing .

Magnetic field due to electrical currents

All moving charged particles produce magnetic fields. Moving point charges,

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