Is it physically possible to substantially change a large magnetic field with a smaller one analogous to the electric field at the gate being able to partially or completely block the flow from source to drain in a transistor? I'm imagining being able to reorient the field from a rare earth magnet using less powerful electromagnets - would this currently be just science fiction?
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Almost. There is a device called a magnetic amplifier in which a small magnetic field is used to control a much larger field by means of a cleverly-designed transformer. At one time it was thought that these could be used in electric power control systems but cheap and reliable transistors took over the market before that happened.
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$\begingroup$ Yes I stumbled across magnetic amplifiers, while interesting my understanding is that they only amplify electronic signals using control of a magnetic field to vary the gain. $\endgroup$ Commented May 15, 2020 at 6:31
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$\begingroup$ Hmm, you are right. I do not think that a "magnetic amplifier" as you define it is possible. $\endgroup$ Commented May 15, 2020 at 6:35
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$\begingroup$ It would be nice if there were a proof though to get it out of my mind -- the original thought behind the question was to be able to switch the magnetic path between a work piece and two opposing poles in order to perform inductive heating (ideally using less energy than required using traditional induction heating) $\endgroup$ Commented May 15, 2020 at 13:13