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# 7.4: Magnetic Moment

If a compass needle, or indeed any bar magnet, is placed in an external magnetic field, it experiences a torque – the one exception being if the needle is placed exactly along the direction of the field. The torque is greatest when the needle is oriented at right angles to the field.

Definition. The magnetic moment of a magnet is equal to the maximum torque it experiences when in unit magnetic field.

As already noted this maximum torque is experienced when the magnet is at right angles to the magnetic field. In SI units, "unit magnetic field" means, of course, one tesla, and the SI units of magnetic moment are $$\text{N m T}^{−1}$$ , or newton metres per tesla. The reader should look up (or deduce) the dimension of magnetic field (teslas) and then show that the dimensions of magnetic moment are $$\text{L}^{2} \text{T}^{−1} \text{Q}$$.

It is noted here that many different definitions of and units for magnetic moment are to be found in the literature, not all of which are correct or even have the correct dimensions. This will be discussed in a later chapter. In the meantime the definition we have given above is standard in the Système International.