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Hall effect

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The idea behind the Hall effect is according to my book that the magnetic field induces a charge distribution such that there is more positive charge on one side and more negative on the other. This induces a potential difference. But the question is: Is this the correct way to view it? I mean after all the charges are never stationary and even so, how is it possible for a magnetic field, which can do no work, to establish a potential difference?

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