# Formula: Magnetic Dipole in a Magnetic Field

## Force

Unit
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

Unit
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

Unit
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.