Question

A bar magnet is moved towards a coil (a) slowly, (b) quickly. The induced EMF is

• A. same in both cases
• B. large in case
• C. large in case
• D. dependent only on radius of the coil

Answer 1

The Correct Option is C

Step 1: Recall Faraday's Law of Electromagnetic Induction.

Faraday's Law states that the induced EMF (\( \varepsilon \)) in a coil is proportional to the rate of change of magnetic flux (\( \phi \)) through the coil:

\[ \varepsilon = -N \frac{d\phi}{dt}, \]

where:

• \( N \) is the number of turns in the coil,
• \( \phi \) is the magnetic flux, and
• \( \frac{d\phi}{dt} \) is the rate of change of magnetic flux with respect to time.

 

The faster the magnet moves, the greater the rate of change of magnetic flux (\( \frac{d\phi}{dt} \)), and hence the larger the induced EMF.

Step 2: Compare the two cases.

• (a) Slowly moving the magnet: When the magnet is moved slowly, the rate of change of magnetic flux is smaller, resulting in a smaller induced EMF.
• (b) Quickly moving the magnet: When the magnet is moved quickly, the rate of change of magnetic flux is larger, resulting in a larger induced EMF.

Step 3: Analyze the options.

• (1) Same in both cases: This is incorrect because the induced EMF depends on the rate of change of magnetic flux, which differs between the two cases.
• (2) Large in case (a): This is incorrect because the induced EMF is smaller when the magnet is moved slowly.
• (3) Large in case (b): This is correct because the induced EMF is larger when the magnet is moved quickly due to the higher rate of change of magnetic flux.
• (4) Dependent only on radius of the coil: This is incorrect because the induced EMF depends on the rate of change of magnetic flux, not just the radius of the coil.

Final Answer: The induced EMF is \( \mathbf{\text{large in case (b)}} \), which corresponds to option \( \mathbf{(3)} \).