Question

A loop is placed in a region where the magnetic field is changing. At t = 0 s the magnetic field is 1 T directed into the page. Over a period of 2 s, the field changes uniformly to 1 T directed out of the page.
Which of the following describes the direction, clockwise (CW) or counterclockwise (CCW), of the induced EMF in the loop?

Answer 1

Answer:

Clockwise

Explanation:

According to Faraday-Newmann-Lenz's law, when there is a change in magnetic flux linkage through a coil, an emf is induced in the coil, and it is given by the equation

$\epsilon=-\frac{Nd\Phi}{dt}$

where

N is the number of turns in the coil

$\frac{d\Phi}{dt}$ is the rate of change of magnetic flux in the coil

The negative sign in the formula indicates the direction of the induced emf, which is such that it opposes the direction of change in magnetic flux that originated the emf.

In this problem:

- At the beginning, the magnetic field is 1 T directed into the page

- Then, this magnetic field changes uniformly to 1 T directed out of the page (opposite direction)

We split the problem into two parts:

- In the first part, the strength of the magnetic field changes uniformly from 1 T to 0. This means that the magnetic flux through the coil is decreasing: therefore, the induced emf must be such that it produces a magnetic field that try to add to the original field. Using the right hand rule (thumb in the direction of the current in the loop and other fingers "wrapped" to give the direction of the field), we see that in order to produce a magnetic field into the page, the current must be clockwise.

- In the second part, the strength of the magnetic field changes uniformly from 0 T to 1 T, but in the direction out of the page. This means that the magnetic flux through the coil is increasing: therefore, the induced emf must be such that it produces a magnetic field that try to subtract to the original field, therefore the new produced field must be into the page (opposite direction to the external field).. Using the right hand rule again, we see that in order to produce a magnetic field into the page, the current must be clockwise again.