# What does it mean to say "a paramagnetic material is attracted to an external magnetic field?"

I'm just having a hard time wrapping my head around what actually goes on when a paramagnetic material is exposed to an external magnetic field. I understand that the individual dipoles line up so that they point in the direction of the field, but why does that need to happen for there to be magnetic attraction? And what exactly is being attracted in the first place? If I imagine the dipoles are caused by little rings of current, are the rings themselves pulled in the direction of the field? Also, what happens if the dipole starts out pointed out in exactly the opposite direction of the external field?

Let me explain the difference using a simple model of an atom - as consisting of electrons revolving in orbits around a heavy nucleus.

When a material is exposed to a magnetic field, the electrons move in such a manner as to oppose it. The material mildly repels the magnetic field.

However, if a material has unpaired electrons, it has a net molecular magnetic moment. An external magnetic field tries to align the molecule moments along its direction while the thermal agitation tries to randomize them. The competition between the ordering effect of the magnetic field and the disordering effect of heat results in a temperature dependent magnetic attraction of the material to the field, called paramagnetism. All materials are diamagnetic while those with unpaired electrons are paramagnetic. When paramagnetism exists, it overshadows diamagnetism by several orders of magnitude.

As alluded by @TZDZ, a complete understanding of magnetism requires a quantum mechanical treatment. However, this simple model usually suffices for a first introduction to the topic.

A paramagnetic material is attracted not by the magnetic field but the force on it is towards the direction in which the magnetic field is increasing. In a constant field it would stay in place. This follows from the simple fact that all systems try to obtain a potential energy minimum.

Magnetic forces are not easy to apprehend. Personally, I dislike magnets, so in a first step I will use coils. Consider two coils $S_1$ and $S_2$ along the $\vec{z}$ axis at a distance $d$ one from each other. They are fed by a current $\vec{i}=I\vec{e_\theta}$. As you know, the magnetic field induced by each coil is like :

The magnetic field from $S_1$ on $S_2$ is $\vec{B}=B_z\vec{z}+B_r\vec{e_r}$. The force is $\vec{i}\wedge\vec{B}=-F\vec{z}$ : the second coil tends to be attracted by the first one. Reciprocally, if the material is diamagnetic, the magnetics domains will oppose the field (much like two magnets with same pole facing), so in my analogy the current of the second coil would be negative : the force would be in the opposite direction (repulsion).

Usually, the force between two magnets or a magnet and a magnetic material is calculate with regard to the energy. The first step is quantifying the energy between the magnets, and the force is deduced from the variation of energy in the volume between the magnets. The energy is lower when magnets are aligned and closer, thus the direction of force. There is a whole article on wikipedia.

With coils, you can see the diminution of magnetic energy as the pooling of the fields of both coils.