Question

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of the magnetic field. The magnetic field is reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms. If the EMFs induced in the two time intervals are \( e_1 \) and \( e_2 \) respectively, then the value of \( e_1 / e_2 \) is:

• A. 1
• B. 3
• C. 2
• D. 4

Hint:

The induced EMF is proportional to the rate of change of magnetic flux. The faster the change, the greater the induced EMF.

Answer 1

The Correct Option is B

The induced EMF \( e \) in a coil is given by Faraday's Law: \[ e = -N \frac{d\Phi}{dt} \] where \( \Phi \) is the magnetic flux, \( N \) is the number of turns, and \( \frac{d\Phi}{dt} \) is the rate of change of magnetic flux. The magnetic flux \( \Phi = B \cdot A \), where \( B \) is the magnetic field and \( A \) is the area of the coil. The area of the coil is: \[ A = \pi r^2 = \pi \left(\frac{15}{2} \, \text{mm}\right)^2 = \pi (7.5 \times 10^{-3})^2 \, \text{m}^2 \] For the first interval, the magnetic field decreases from 30 mT to 0 mT, and for the second interval, it increases from 0 mT to 30 mT. The induced EMF is proportional to the rate of change of magnetic field, so the ratio of induced EMFs will be the inverse of the time intervals: \[ \frac{e_1}{e_2} = \frac{20 \, \text{ms}}{40 \, \text{ms}} = 3 \] Therefore, the correct answer is (B).