# Encyclopedia of magnetics and electromagnetics

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# Magnetic dipole moment

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

## 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)

 Support us with just $1.00 through PayPal or a credit card: Magnetic dipole moment$\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 ## 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 energyU$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) 