magnetic_dipole_moment

Stan Zurek, Magnetic dipole moment , Encyclopedia-Magnetica.com, {accessed 2020-10-20} |

**Magnetic dipole moment** or **magnetic moment** (often denoted by letter ** m** or $\mu$)

The magnetic dipole moment is a product of the amplitude of the current $I$ and the area $A$ of the loop: ^{4)}

$$ \vec m = \vec I · A $$ | (A·m²) |

Magnetic moment is a pseudovector^{5)} and a force or torque acts on the “centre of mass” of the dipole.^{6)}

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Magnetic dipole moment $\vec m$ of a loop of current $\vec I$ with the loop area $A$

^{by S. Zurek, Encyclopedia Magnetica, CC-BY-3.0}

^{by S. Zurek, Encyclopedia Magnetica, CC-BY-3.0}

If the current loop is exposed to magnetic field, in the form of magnetic flux density (vector of *B*) then the magnetic moment allows calculation of the torque $\tau$, which will tend to align the current loop parallel to the applied *B*. This torque has an energy associated with it:^{7)}

$$ \vec \tau = \vec m \times \vec B $$ | (N·m) = (J) |

The mechanical energy $U$ associated with a magnetic dipole moment *m* placed in magnetic field *B* is:^{8)}^{9)}

$$ U = - \vec m \cdot \vec B $$ | (J) |

If the current loop is placed in a gradient of flux density $B$ then the magnetic dipole moment allows calculation of the force $F$ which will attract or repel it (depending on the mutual alignment of the vectors of B and m), for a general three-dimensional case:^{10)}

$$ \pmb { F = \nabla ( m \cdot B ) } $$ | (N) |

and simplified for a single axis *x*:^{11)}

$$ F = m \frac{d B}{ d x} $$ | (N) |

magnetic_dipole_moment.txt · Last modified: 2020/10/17 15:38 by stan_zurek