Question

A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:

• A. 5 V
• B. 3.5 V
• C. 2.5 V
• D. Zero V

Hint:

When calculating induced emf using Faraday's Law, always use the rate of change of magnetic flux. For rotational motion, remember to consider the angle change during the motion.

Answer 1

The Correct Option is C

We use Faraday's law of electromagnetic induction, which states that the induced emf is given by the rate of change of magnetic flux through the loop: \[ \mathcal{E} = - \frac{d\Phi}{dt} \] where \( \Phi = B A \cos(\theta) \) is the magnetic flux.
Here, \( B = 0.4 \, \text{T} \), \( A = (0.50)^2 \, \text{m}^2 = 0.25 \, \text{m}^2 \), and the angle \( \theta \) changes from 0° to 60°.
We can calculate the change in flux \( \Delta \Phi \): \[ \Delta \Phi = B A (\cos(0^\circ) - \cos(60^\circ)) = 0.4 \times 0.25 \times (1 - \frac{1}{2}) = 0.4 \times 0.25 \times 0.5 = 0.05 \, \text{Wb} \] The time taken is \( \Delta t = 0.2 \, \text{s} \). Therefore, the induced emf is: \[ \mathcal{E} = \frac{\Delta \Phi}{\Delta t} = \frac{0.05}{0.2} = 0.25 \, \text{V} \] Thus, the induced emf is 2.5 V. Final Answer: (C) 2.5 V