# Why is a paramagnetic material attracted into a magnetic field?

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.

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I think there is some confusion here. The actual field direction does not play a role for diamagnetic or paramagnetic behavior. What is important is the field strength. What is actually ment by Griffith is: "The paramagnet is attracted into the region of higher field magnitude." In a simlified picture it goes into regions where the field lines are more dense, while a diamagnet lowers its energy by going into regions of lower field line density. You got it, hence, almost right already.

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I think that is what I was confused about. I read "into the field", as the direction opposite of the direction the field is going. This makes a lot more sense. Thanks! –  user35734 Dec 13 '13 at 17:14

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.

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