# An emf is induced in response to a change in the magnetic field inside a loop of wire. Which of...

## Question:

An emf is induced in response to a change in the magnetic field inside a loop of wire. Which of the following changes would increase the magnitude of the induced emf?

A. reducing the diameter of the loop

B. reducing the resistance of the wire of which the loop is made

C. turning the plane of the loop to be parallel to the magnetic field

D. changing the magnetic field more rapidly

According to Faraday's second law of electromagnetic induction, the magnitude of induced emf on a coil is directly proportional to the rate of change of magnetic flux linked with the coil.

We know that the magnetic flux linked with a coil is given by

{eq}\begin{align} \Phi = BA \cos \theta \\ \Phi = BA \cos \omega t \end{align} {/eq}

As per Faraday's second law, the magnitude of induced emf on a coil is directly proportional to the rate of change of magnetic flux linked with the coil. so magnetic flux can be changed by either way

1. By changing magnetic field B
2. By changing area A and
3. By changing {eq}\theta {/eq} i.e. by rotating the coil.

So Option D) Changing the magnetic field more rapidly will definitely increase the magnitude of the induced emf. is correct.

Option A Wrong because reducing diameter decreases the area and causes induced emf but the magnitude of the induced emf depends upon how fast the diameter reduces or changes.

Option B Wrong because reducing the resistance of the wire increases the induced current but not the induced emf.

Option C Wrong because the magnitude of the induced emf depends upon how fast we turn the plane.