Question

An increase in magnetic flux through a coil of 500 turns in 0·1 s is 0·001 Wb. The maximum induced EMF generated in the coil is

• A. 50 V
• B. 10 V
• C. 0·5 V
• D. 5 V

Answer 1

The Correct Option is D

To determine the maximum induced EMF (Electromotive Force) in a coil when the magnetic flux changes, we use Faraday's law of electromagnetic induction. Faraday's law states that the induced EMF in a coil is equal to the rate of change of magnetic flux through the coil multiplied by the number of turns in the coil.

The formula for the induced EMF (\( \mathcal{E} \)) is:

\( \mathcal{E} = -N \frac{\Delta \Phi}{\Delta t} \)

 

Where:

• \( N \) is the number of turns in the coil.
• \( \Delta \Phi \) is the change in magnetic flux (in Weber, Wb).
• \( \Delta t \) is the time interval over which the change occurs (in seconds, s).

Given:

• \( N = 500 \) turns
• \( \Delta \Phi = 0.001 \) Wb
• \( \Delta t = 0.1 \) s

Substituting these values into the formula:

\( \mathcal{E} = -500 \cdot \frac{0.001}{0.1} \)

 

\( \mathcal{E} = -500 \cdot 0.01 \)

 

\( \mathcal{E} = -5\, \text{V} \)

 

Since the question asks for the maximum induced EMF and EMF is a scalar quantity, we take the absolute value:

Maximum induced EMF = 5 V

 

Therefore, the maximum induced EMF generated in the coil is 5 V.

Answer 2

According to Faraday's Law of Electromagnetic Induction, the induced EMF is given by:

\[ \text{EMF} = \frac{N \cdot \Delta \Phi}{\Delta t} \]

Where:

• \( N = 500 \) (number of turns)
• \( \Delta \Phi = 0.001 \, \text{Wb} \) (change in magnetic flux)
• \( \Delta t = 0.1 \, \text{s} \)

Substituting the values:

\[ \text{EMF} = \frac{500 \times 0.001}{0.1} = \frac{0.5}{0.1} = 5 \, \text{V} \]

Correct Answer: 5 V