Chapter 21, Problem 1P

To determine

The EMF induced in the coil.

Answer to Problem 1P

Solution:

The EMF induced in the coil is equal to -564.7 V.

Explanation of Solution

According to Faraday’s law, any change in the magnetic environment of a coil will cause an induced EMF.

The induced EMF in a coil is equal to the negative rate of change of the magnetic flux times the number of turns in the coil.

Given:

The flux changes form $-58\text{ Wb}$ to $38\text{ Wb}$ .

The time taken is 0.34 s.

Formula used:

The expression for the EMF is as follows:

  $\epsilon =-N\frac{d\varphi }{dt}$

Here, $d\varphi$ is the change in the flux, $dt$ is the change in time, N is the number of turns.

The equation is rewritten as follows:

  $\epsilon =-N\frac{{\varphi }_2-{\varphi }_1}{dt}$

Here, ${\varphi }_2$ is the final flux and ${\varphi }_1$ is the flux initially.

Calculation:

Substitute $-58\text{ Wb}$ for ${\varphi }_1$ , $38\text{ Wb}$ for ${\varphi }_2$ , 2 for N , and 0.34 s for $dt$ in the equation $\epsilon =-N\frac{{\varphi }_2-{\varphi }_1}{dt}$ .

  $\begin{array}{c}\epsilon =-\left(2\right)\frac{38\text{ Wb}-\left(-58\text{ Wb}\right)}{38\text{ Wb}}\end{array}$

   $\begin{array}{c}=-\left(2\right)\frac{38\text{ Wb}-\left(-58\text{ Wb}\right)}{0.34\text{ s}}\end{array}$

   $\begin{array}{c}=-564.7\text{ V}\end{array}$

Conclusion:

Hence, the EMF induced is equal to -564.7 V.