# Is there energy stored when iron is magnetized?

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?

• Yes. Energy is stored. A compact answer is here van.physics.illinois.edu/qa/listing.php?id=17858 . – anna v Oct 16 '13 at 3:29
• @annav I've read the source, very useful thank you! However, Is the energy stored(from the energy density) in the field equal to the energy applied to align the domains? And is it equal to the energy needed to demagnetize the domains? Example, say a magnet's magnetic field has stored energy of 50J, that means it can do work that is equal to 50J on ferromagnets, in order to demagnetize the magnet do we apply the same amount? Or even demagnetize the ferromagnets that are attracted to the magnet? – AxtII Oct 16 '13 at 14:06
• Energy is conserved, therefore atleast that much energy must be supplied as the one that exists in the ordered domains, but in general there is always some loss in recovering stored energy, to heat , to radiation or to motion, depending on the method of recovery. – anna v Oct 16 '13 at 16:35
• @annav I agree. However, is the total energy of the system composed of multiple sources? For example: The energy that is required to magnetize the ferromagnet & The energy stored in the field to do work on other ferromagnetic objects like attracting them etc... = Net total energy stored? Because it seems the magnetization by itself is a process that requires energy. And the phenomenon of attraction also requires energy of its own. So I assume the total energy conserved is composed of E1 + E2 + E3 = E total. – AxtII Oct 16 '13 at 18:19
• @annav For some reason I believe that the energy required to magnetized a soft iron ferromagnet is not equal to the amount of energy applied to attract it by an exterior magnetic field. So that's why I assume the energy is a net total of adding them up or something like that. – AxtII Oct 17 '13 at 5:00

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.

Well you probably should check on this, but if I am not mistaken, the (ferro) magnetized state is actually a lower energy state. I believe there is a process called "adiabatic demagnetization" that is actually used to reach lower cryogenic temperatures. Well like I said; check it out.

• "A bulk piece of ferromagnetic material in its lowest energy state has little or no external magnetic field. The material is said to be "unmagnetized"." - Wikipedia – AxtII Oct 16 '13 at 1:59
• This is confusing. There is the "Ex" exchange energy that is lowest when the domains all point in the same direction... "It is lowest when the dipoles are all pointed in the same direction, so it is responsible for magnetization of magnetic materials. When two domains with different directions of magnetization are next to each other, at the domain wall between them magnetic dipoles pointed in different directions lie next to each other, increasing this energy. This additional exchange energy is proportional to the total area of the domain walls." - Wikipeida – AxtII Oct 16 '13 at 2:05
• Sounds confusing to me too V-XCIX. Seems like my memory could have it backwards. I don't do Wikipedia; but if you like it, check out the adiabatic demagnetization angle. But Anna usually has it straight. – user26165 Oct 16 '13 at 8:01
• this is another question, i.e., "what is the minimum energy state of ferromangetic materials .From this link hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html it seems that the theoretical formulation of how domains under the influence of an external field reorient themselves is still under investigation. The statement about random orientation having the minimum energy is correct: think of two permanent magnets, it takes energy to keep them parallel, they tend to end up north to south, no? The wiki article goes on to talk about stable secondary minima due to crystal structure. – anna v Oct 18 '13 at 4:36

I think the correct answer is it store "lower entropy state", not the energy

• Hi Thaina, can you please expand and clarify your answer? – Brandon Enright Dec 17 '13 at 5:19
• Magnet is ordered atom of iron, lower entropy means lower chaotic. It relate to energy of the system that lower entropy can be converted to energy. Like you have water store in high ground – Thaina Dec 17 '13 at 11:01