# Finding the magnetic moment of a permanent magnet to calculate the torque when exposed to a magnetic field

A permanent magnet has a magnetic moment $m$ associated with it. When exposed to a magnetic field $B$ the torque acting on the magnet can be calculated as $\tau = m \times B$.

I am trying to calculate the torque imposed on a disc magnet in a magnetic field with a known strength. However, I do not know the magnetic moment of the magnet. How can the magnetic moment of a permanent be calculated?

So far I have the datasheet (link) of the magnet I would like to use which contains the following magnetic properties: Magnetisation Grade, Residual magnetism, Coercive field strength bHc, Coercive field strength iHc and the energy product. However, I cannot seem to find the magnetic moment using these properties.

Any suggestions or hints?

It is 1 mm high and has a "residual magnetism" of 1.4 T. I think that might be enough to estimate the dipole moment as we know that the magnetic field along the axis of a dipole goes as

$$B = \frac{\mu_0}{2\pi r^3}\vec{m}$$

Putting $r = 1$ mm, $\mu_0 = 4\pi\cdot 10^{-7}$H/m, and $B = 1.4$ T, we find

$$m = \frac{2\pi r^3 B}{\mu_0} = 7 \cdot 10^{-3}\;\mathrm{Nm/T}$$

This may be inaccurate because the magnet is relatively large - so approximating it as a small rod is probably too simplistic (the field will drop off more slowly initially as the area is large).

If you could measure the torque experienced by a needle-like metallic object with known magnetic properties, you could do a much better job at estimating this.

Wikipedia states that the magnetic dipole moment of a permanent magnet is related to the residual magnetism by the volume of the magnet. The formula is:

$$m = \frac{1}{\mu_0}B_r V$$

Assuming this is correct, you'd need the radius as well as the height of the magnet to calculate the volume, and then the magnetic moment is proportional by $$\frac{B_r}{\mu_0}$$.