Question

When a loop moves towards a stationary magnet with speed $v$, the induced emf in the loop is $E$. If the magnet also moves away from the loop with the same speed, then the emf induced in the loop is

• A. $E$
• B. $2E$
• C. $\frac{E}{2}$
• D. Zero

Answer 1

The correct option is D

Zero

Step 1: Faraday's law

1. Faraday's law states that the emf is induced due to the change in magnetic flux.
2. Both the loop and the magnet are moving at the same speed and in the same direction.
3. Hence, the relative velocity between the loop and the magnet is zero, or the change in magnetic flux is zero.

Step 2: Equation for Faraday's law

The equation for Faraday's law can be written as follows:

$E=-N\frac{∆{\varphi }_M}{∆t}$

Here, $E$ is the induced e.m.f, $∆{\varphi }_M$ is the change in magnetic flux, $N$ is the number of loops, and $∆t$ is the change in time.

Since the change in magnetic flux is zero, the equation becomes as follows:

$$\begin{gathered} E=-N\times \frac{0}{∆t} \\ E=0 \end{gathered}$$

Therefore, the emf induced in the loop is zero.

Hence, option (D) is correct.