Question

The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside uniform magnetic field 
B. moving the coil with non uniform speed inside uniform magnetic field 
C. rotating the coil inside the uniform magnetic field 
D. changing the area of the coil inside the uniform magnetic field 
Choose the correct answer from the options given below :

• A. B and D only
• B. C and D only
• C. B and C only
• D. A and C only

Answer 1

The Correct Option is B

Electromagnetic Induction Problem 

Step 1: Faraday's Law of Electromagnetic Induction

Faraday's law states that an emf is induced in a coil when the magnetic flux through the coil changes with time.

Step 2: Magnetic Flux

Magnetic flux (\( \Phi \)) is given by:

\( \Phi = \vec{B} \cdot \vec{A} = BA \cos \theta \)

where \( \vec{B} \) is the magnetic field, \( \vec{A} \) is the area vector of the coil, and \( \theta \) is the angle between the magnetic field and the area vector.

Step 3: Analyze Options

• A. Moving with uniform speed: If the coil moves with uniform speed in a uniform magnetic field, the flux remains constant (assuming the orientation of the coil relative to the field remains unchanged). Therefore, no emf is induced.
• B. Moving with non-uniform speed: Similar to case A, if the orientation doesn’t change with respect to the field, a non-uniform speed doesn’t change the flux. Thus no emf is induced.
• C. Rotating the coil: When the coil rotates in a uniform magnetic field, the angle between the magnetic field and the area vector changes. This changes the magnetic flux, inducing an emf.
• D. Changing the area: Changing the area of the coil directly changes the magnetic flux, inducing an emf.

Conclusion:

An induced emf can be produced by rotating the coil (C) and by changing the area of the coil (D) (Option 2).

Induced emf can be induced in a coil by changing magnetic flux. And 𝜙 = 𝐵⃗ . 𝑑𝐴⃗⃗⃗⃗⃗ By rotating coil, angle between coil and magnetic field changes and hence flux changes. By changing area, magnetic flux changes.