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Why is it that if a conductor 'cuts through' (what does this mean?) a magnetic field that a potential difference is produced?

I read this recently in a textbook...

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The conductor is a metal and hence it has free electrons. These free electrons are charge carriers and therefore when influenced by a magnetic field (i.e. the magnetic field exerts a force on the electrons), they move to create a potential difference in the conductor. This effect is even more greatly amplified, when the field lines of the magnet are perpendicular to the conductor, hence the term 'cut across'.

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