Question

A coil is placed in a changing magnetic field and an emf is induced. What happens to the induced emf if the rate of change of magnetic field quadruples?

A. The emf quadruples.
B. The emf doubles.
C. The emf halves.
D. There is no change.
E. The emf increases by a factor of 16.

Answer 1

If the rate of change of the magnetic field quadruples, the induced emf in the coil also quadruples, as the induced emf is directly proportional to the rate of change of magnetic flux through the coil according to Faraday's law.

Step-by-step explanation:

When a coil is placed in a changing magnetic field, Faraday's law of electromagnetic induction describes that an induced emf (electromotive force) is generated in the coil, which is directly proportional to the rate of change of the magnetic flux through it. If the rate of change of the magnetic field quadruples, the induced emf in the coil also quadruples. According to Faraday's law, the emf induced in a loop is given by 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 Φ. Therefore, if the rate of changing magnetic field quadruples, the rate of change of magnetic flux through the coil quadruples as well, leading to a quadrupled induced emf.