Magnetic Moment - Units


The unit for magnetic moment is not a base unit in the International System of Units (SI) and it can be represented in more than one way. For example, in the current loop definition, the area is measured in square meters and I is measured in amperes, so the magnetic moment is measured in ampere–square meters (A m2). In the equation for torque on a moment, the torque is measured in joules and the magnetic field in tesla, so the moment is measured in Joules per Tesla (J⋅T−1). These two representations are equivalent:

1 A·m2 = 1 J·T−1.

In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, Gaussian, and EMU. Among these, there are two alternative (non-equivalent) units of magnetic dipole moment in CGS:

(ESU CGS) 1 stat A·cm2 = 3.33564095×10−14 (A·m2 or J·T−1)

and (more frequently used)

(EMU CGS and Gaussian-CGS) 1 erg/G = 1 abA·cm2 = 10−3 (m2·A or J/T).

The ratio of these two non-equivalent CGS units (EMU/ESU) is equal exactly to the speed of light in free space, expressed in cm·s−1.

All formulas in this article are correct in SI units, but in other unit systems, the formulas may need to be changed. For example, in SI units, a loop of current with current I and area A has magnetic moment I×A (see below), but in Gaussian units the magnetic moment is I×A/c.

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