[Physics] Is there energy stored when iron is magnetized

electromagnetismmagnetic fieldsmagnetic-momentpotential energy

When a piece of iron is magnetized, and the domains are aligned,
Is there energy stored? If so, how much energy is stored?
If there is an attraction between that same iron and the source of the exterior magnetic field,where work is done, and there is energy that is transferred. Is the energy equal to that of which is stored in the alignment of the domains?

And how much energy is stored or needed to align the domains?

Best Answer

I believe the term you're looking for is "Magnetostatic Energy". Magnetostatics is the field that studies static (constant) magnetic fields, much like electrostatics.

For a uniform material the magnetostatic stored potential energy is:

$$E_{\mathrm{ms}} = \frac{1}{2}\mu_0 \int_V \mathbf{M} \cdot \mathbf{H}_{\mathrm{ms}} d^3 r$$

You can find a full derivation here. The Wikipedia article on magnetic domains also covers a lot of details about the field energy.