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If you had a powerful electromagnet in the shape of a hollow sphere in which the top and bottom halves are the opposing poles, what can the magnetic filed at the center of the sphere be used for?

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First, the question is irrelevant to the subject.

Second, answer to the question is, the magnetic field inside the hollow sphere is zero. As, all the magnetic lines of force pass through the body.

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Cold fusion could be an application

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Not my downvote (but probably deserved). Why would cold fusion require large magnetic fields? – Ron Maimon Aug 31 '12 at 17:19
Cant it be used as a form of excitation or catalyst for the reaction? – Alex Voinescu Aug 31 '12 at 18:33

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