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Does speed of magnet’s rotating affect electricity

A note about terminology – “electricity” is a very ambiguous term, as it describes many interrelated phenomena, but not one thing in particular. You probably mean current in this case, as in a standard electrical generator.

In such a case, yes. There are four major equations that govern classical EM. One of them,

EMF=-d(B*A)/dt

governs this situation. Consider a loop of wire enclosing area A near a rotating magnet, such that the magnet rotates to face toward and then away from the loop. In this case, the flux is proportional to the field strength. Since the derivative of the flux depends on the rate of change of the magnetic field, spinning the magnet faster will give a higher current in the loop.

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