Chapter 31, Problem 1OQ

To determine

The rank of the emf induced in the coil at the instants marked $\text{A}$ through $\text{E}$ from the largest positive value to the largest-magnitude negative value.

Answer to Problem 1OQ

The rank of the emf induced in the coil at the instants marked $\text{A}$ through $\text{E}$ from the largest positive value to the largest-magnitude negative value is $\text{E>A>B=D>C}$.

Explanation of Solution

Write the expression for induced emf by Faraday’s law.

    $\epsilon =-\frac{d\varphi }{dt}$

Here, $\epsilon$ is the induced emf, $dt$ is the time elapsed and $d\varphi$ is the change in magnetic flux.

The above equation signifies that the induced emf is directly proportional to the negative of flux that is, the induced emf will have a maximum positive value when the flux has a maximum negative value and vice versa.

The induced emf at point $\text{E}$ will have the largest positive value, then next to it is $\text{A}$,  $\text{B}$ and $\text{D}$, it will be zero and at point $\text{C}$, it will have largest negative value.

Conclusion:

Therefore, the rank of the emf induced in the coil at the instants marked $\text{A}$ through $\text{E}$ from the largest positive value to the largest-magnitude negative value is $\text{E>A>B=D>C}$.