Question

A coil having an area of \( 2 \, \text{m}^2 \) is placed in a magnetic field which changes from 1 Wb/m² to 4 Wb/m² in 2 seconds. The emf induced in the coil will be:

• A. 4 V
• B. 3 V
• C. 2 V
• D. 1 V

Hint:

The induced emf is directly proportional to the rate of change of magnetic flux through the coil.

Answer 1

The Correct Option is B

Step 1: Understand the formula for induced emf.
The induced emf \( \varepsilon \) in a coil due to a changing magnetic field is given by Faraday's law of electromagnetic induction: \[ \varepsilon = - \frac{d\Phi}{dt} \] where \( \Phi = B \times A \) is the magnetic flux, \( B \) is the magnetic field strength, \( A \) is the area of the coil, and \( \frac{d\Phi}{dt} \) is the rate of change of magnetic flux.

Step 2: Calculate the change in magnetic flux.
The magnetic flux at any instant is given by: \[ \Phi = B \times A \] Initially, \( B_1 = 1 \, \text{Wb/m}^2 \) and finally, \( B_2 = 4 \, \text{Wb/m}^2 \). The area \( A = 2 \, \text{m}^2 \). So, the change in magnetic flux is: \[ \Delta \Phi = (B_2 - B_1) \times A = (4 - 1) \times 2 = 6 \, \text{Wb} \]

Step 3: Calculate the induced emf.
Now, the time interval \( \Delta t = 2 \, \text{seconds} \). The induced emf is: \[ \varepsilon = - \frac{\Delta \Phi}{\Delta t} = - \frac{6}{2} = 3 \, \text{V} \]

Step 4: Conclusion.
The induced emf in the coil is 3 V, which is option (2).