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magnetic_dipole_moment

Magnetic dipole moment

Definition

Magnetic dipole moment or magnetic moment (often denoted by letter m or $\mu$)1)2) - a vector quantifying the magnetic property of a current loop. The direction of magnetic moment $\vec m$ is defined by the right-hand rule and is perpendicular to the plane of the loop.3)

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 pseudovector5) 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

Magnetic field strength $\vec H$ associated with the current loop

by S. Zurek, Encyclopedia Magnetica, CC-BY-3.0

Field lines around magnetic dipole and electric dipole are similar
by Geek3, CC-BY-SA-3.0

Magnetic dipole moment in magnetic field

Torque

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)

Energy

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)

Force on single dipole

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)

See also

References

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

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