I want to start by saying I've seen this topic: Attraction and repulsion of Magnetic materials and its supposed duplicates and it hasn't helped me very much.
In the book Introduction to Electrodynamics by Griffiths, it says the following:
"In general, when a sample is placed in a region of nonuniform field, the paramagnet is attracted into the field, whereas the diamagnet is repelled away." (section 6.14, p.273, 4th ed.)
I don't understand why this should be true. The book states that the reasons for paramagnetism and diamagnetism are due to quantum mechanics, but the book seems to imply there is a classical reason as well.
The only thing I can think of is the equation that in a nonuniform magnetic field, $F=\nabla(m \cdot B)$. Now if the $B$ field is getting weaker if you continue in the direction the field is in at that point (and stronger if you go the reverse direction), then for a paramagnetic material, with $m$ lined up with $B$ the direction of $F=\nabla(m \cdot B)$ is into the field, and for a diamagnetic field, $F=\nabla(m \cdot B)$ is away from the field. But I don't see any reason why the $B$ field gets weaker as you continue along the direction of the $B$ field.
Any help would be very appreciated.
Best Answer
I can give you a simplified picture:
The external magnetic field induces in the atoms of a diamagnetic material a current, which produces a magnetic field in the opposite direction (Lenz's law). Because of this effect, the diamagnet is repelled away.
The same effect takes place in an paramagnet, but here is another effect stronger: Due to the magnetic moment of the unpaired electrons in the material there accures an total magnetisation in the direction of the external field.
This does not occur in diamagnetic material because there are no unpaired electrons.
I hope it helped.