Question

A coil of an AC generator, having 100 turns and area 0.1 m² each, rotates at half a rotation per second in a magnetic field of 0.02 T. The maximum emf generated in the coil is:

• A. 0.31 V
• B. 0.20 V
• C. 0.63 V
• D. 0.10 V

Hint:

The maximum induced emf in a rotating coil depends on the number of turns, the area of the coil, the strength of the magnetic field, and the angular velocity of the coil.

Answer 1

The Correct Option is A

Step 1: The Formula 

The maximum emf induced in a coil rotating in a magnetic field is given by: \[ \text{emf}_{\text{max}} = N A B \omega \] Where:

• \( N \) is the number of turns of the coil,
• \( A \) is the area of the coil,
• \( B \) is the magnetic field strength,
• \( \omega \) is the angular velocity.

Step 2: Applying the Values

Given values:

• Number of turns \( N = 100 \),
• Area \( A = 0.1 \, \text{m}^2 \),
• Magnetic field strength \( B = 0.02 \, \text{T} \),
• Angular velocity \( \omega = 2\pi \times 0.5 = \pi \, \text{rad/s} \).

Substituting these values into the formula: \[ \text{emf}_{\text{max}} = 100 \times 0.1 \times 0.02 \times \pi = 0.31 \, \text{V} \]

 

Conclusion:

The maximum emf induced in the coil is \( 0.31 \, \text{V} \), corresponding to the correct option.