# Encyclopedia Magnetica™

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magnetic_dipole_moment

# Magnetic dipole moment

 Stan Zurek, Magnetic dipole moment, Encyclopedia Magnetica, https://e-magnetica.pl/doku.php/magnetic_dipole_moment

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

This convention defines the polarity of magnetic poles, with the sense of the arrow denoting magnetic north pole.4)

Magnetic dipoles are used as the basis for the definition of magnetisation M (response of matter to being magnetised).

Magnetic dipole moment $\vec m$ of a loop of current $\vec I$ with the loop area $A$ and unit vector $\vec a$ (normal to $A$)

The magnetic dipole moment is a product of the amplitude of the current $I$ and the area $A$ of the loop: 5)

 $$m = I · A$$ (A·m²)

The vector $\vec m$ is oriented in the same direction as the unit vector $\vec a$, normal to the surface $A$:

 $$\vec m = I · A · \vec a$$ (A·m²)

Magnetic moment is a pseudovector6) and a force or torque acts on the “centre of mass” of the dipole.7)

The current loop is known as “magnetic dipole” because of the similarity of the character of the field to that of an electric dipole. In some cases, a similar logic can be applied for analysis of the fields and a magnetic dipole can be represented as a field of two hypothetical separated magnetic monopoles:8)

 $$m = p · l$$ (A·m²)

where: $p$ - strength of magnetic monopoles (A·m), $l$ - distance between the poles (m).

### Calculator of magnetic moment emu (convert between CGS and SI)

This section is an interactive calculator.

Conversion of emu (electromagnetic unit of magnetic moment) from CGS to SI units requires the following numerical scaling:

 $$1 \bigg( emu = \frac{ \text{erg} } { \text{Oe} } \bigg)_{CGS} = 4·π·10^{-10} \bigg( \text{Wb·m} \bigg)_{SI}$$

emu CGS = (≡ erg/Oe)             m·μ0 SI =

Note: emu converted from CGS to SI still represents the magnetic dipole moment m but additionally multiplied by the absolute permeability of vacuum μ0 (which is reflected in the resulting SI units).