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"Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field".

Broadly speaking, all atoms, and molecules, and matter, has an electromagnetic field. Does this imply that a paramagnetic material is weakly, and to a varying degree, attracted to everything?

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Not really. Non-magnetic materials don't produce a net magnetic field, because the magnetism from their individual particles don't align to give substantial total fields, but rather cancel out on average.

But if 'to a varying degree' you're willing to consider ridiculously small attraction forces, then we should consider that this cancellation isn't always perfect. If you have $N$ magnetic particles that can each point up or down (and do so independently of each other, which is a key assumption that won't always hold), then you'll almost never have exactly $N/2$ pointing up and $N/2$ pointing down. On average you'll have an excess of $\sim\sqrt{N}$ particles pointing in one direction or the other, and so there will be a small net magnetic field. This effect becomes bigger for smaller numbers of particles, and is relevant in NMR spectroscopy (where it's called statistical polarization). Thus I suppose there would be a tiny attractive force to any nearby paramagnet.

I should add as a disclaimer that I'm not sure whether statistical polarization would be the dominant contribution in a realistic scenario, but it's one that should be pretty universal.

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