What is the relation between electric magnets and permanent magnets? I just read that a  magnetic field is generated when electrically charged particles move around. If I understand it correctly, the electric field and the magnetic field are two sides of the same coin, namely the electromagnetic field, and the magnetic field is simply defined as the difference between the actual electromagnetic field and what the electromagnetic field would be if everything was at rest. This difference is generated by strange quantum effects that I dont understand.
However what confuses me in this is, why then do permanent magnets interact with the magnetic field, given that they don't containg electrical currents as in an electric magnet? 
 A: The energy of a magnetic moment $\vec{\mu}$ in a magnetic field $\vec{B}$ is given by $$E = - \vec{\mu} \cdot\vec{B}$$
There are the following contributions to the magnetic moment of an atom:


*

*The "rotation" of the electron around the nucleus, which is similar to an electric current. This is called the orbital angular momentum $L$.

*The spin of the electron $S$. This can be thought of as an internal rotation of the electron around itself.

*Finally, the nuclear spin $I$. This is analog to the electron spin, but here the nuclei rotate around themselves. However, this is usually small compared to the other two contributions.


So two magnets interact, because they both poses magnetic moments. Therefore, ...


*

*the first magnetic moment creates a B-field at the position of the second magnet. Hence, the energy of the second magnet changes to to the upper formula.

*However, the problem is symmetric. Therefore, the second magnetic moment creates a B-field at the position of the first magnet, as well. Hence, the energy of the first magnet changes to to the upper formula.

A: "why then do permanent magnets interact with the magnetic field, given that they don't contain electrical currents as in an electric magnet?"
Why do you think there are no electrical currents? Isn't the electron "orbiting" the nucleus? The currents of the electrons of the atoms create the permanent magnet.  You can't use this currents to extract work, but they're there. 
