Chapter 25, Problem 1CQ

To determine

To explain: Whether the induced current exists in the loop or not when the flux through the loop is zero.

Answer to Problem 1CQ

The induced current doesn’t exist in the loop when the flux through the loop is zero.

Explanation of Solution

Formula used:

Consider the equation for induced current.

$I=\frac{\epsilon }{R}$ (1)

Here,

$\epsilon$ is the emf due to motion of conductor.

$R$ is the resistance.

Consider the equation for emf.

$\epsilon =\frac{\Delta \varphi }{\Delta t}$ (2)

Here,

$\Delta \varphi$ is the change in magnetic flux.

$\Delta t$ is the change in time.

Explanation:

Substitute equation (2) in equation (1),

$I=\frac{\left(\frac{\Delta \varphi }{\Delta t}\right)}{R}$

$I=\frac{\Delta \varphi }{\Delta t}\times \frac{1}{R}$ (3)

The magnetic flux through the coil of wire is zero that is,

$\Delta \varphi =0$,

Substitute 0 for $\Delta \varphi$ in equation (3)

$\begin{array}{c}I=\frac{0}{\Delta t}\times \frac{1}{R}\\ =0\text{A}\end{array}$

Since the magnetic field in the coil is zero, so the induce current in the coil will also be zero.

Conclusion:

Hence, the induced current doesn’t exist in the loop when the flux through the loop is zero.