Alexander Fufaev

Formula: Magnetic Dipole in a Magnetic Field

Magnetic Dipole in a Magnetic Field


Force on a magnetic dipole in an external magnetic field \(\class{violet}{\boldsymbol{B}}\). The force can also be written as follows: \[ \boldsymbol{F} ~=~ \boldsymbol{\mu} \, \nabla \class{violet}{\boldsymbol{B}} \]

So the force is determined by the gradient of the magnetic field: \(\nabla \boldsymbol{B}\). Here \(\nabla\) is the nabla operator.

Magnetic dipole moment

Magnetic dipole moment is a measure for the "strength" of a magnetic dipole. Here the scalar product between \(\boldsymbol{\mu}\) and \(\class{violet}{\boldsymbol{B}}\) is formed.

The \(\boldsymbol{\mu}\) vector points in the same direction as the normal vector \(\boldsymbol{A}\). Dipole moment is therefore orthogonal to the surface enclosed by the current loop.

Magnetic flux density

The external magnetic field in which the magnetic dipole is located. If the magnetic field is homogeneous, the magnetic dipole does not experience a force (but only a torque). In an inhomogeneous field, however, the dipole moves in the direction of the larger magnetic field.