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Helmholtz Coils

A Helmholtz coil consists of a pair of similar coils, each with a small cross-section through the wire compared to its overall diameter. The coils are mounted on a common axis, at a fixed distance apart (at or about half the average coil diameter). A number of variations exist, including use of rectangular coils, and other numbers of coils than two. In a two-coil Helmholtz pair connected in series, if electric current is passed through them, a very uniform magnetic field is generated in the space between the coils. At the center, the first, second, and third derivatives of the field all vanish. Helmholtz coils are often used to measure magnets, rather than to create a field. In order to do this, the coil pair is connected to a fluxmeter, which integrates voltage over time.

By Faraday's law:

And so:
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