Question

Two coils of wire are identical except that coil A has twice as many turns of wire as coil B. If a magnetic field increases with time at the same rate through both coils, which coil, if either, has the larger induced voltage?

Answer 1

Coil A, with twice as many turns as coil B, will have a larger induced voltage when both are exposed to the same rate of change in a magnetic field, as per Faraday's Law of electromagnetic induction.

Step-by-step explanation:

The question deals with the concept of electromagnetic induction, specifically how the number of turns in a coil affects the induced voltage when exposed to a changing magnetic field. According to Faraday's Law of electromagnetic induction, the induced voltage in a coil is directly proportional to the rate of change of magnetic flux and the number of turns in the coil. Therefore, if coil A has twice as many turns as coil B, and both are subjected to the same rate of change in magnetic field, coil A would have a larger induced voltage.

This is because the induced emf (electromotive force) in a coil is given by the equation emf = -N (dΦ/dt), where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux through the coil. Hence, with double the turns, coil A induces double the voltage of coil B under identical changing magnetic field conditions.