Question

What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e.m.f. produced in it?

• A. \( \pi \)
• B. \( \frac{\pi}{2} \)
• C. \( \frac{\pi}{4} \)
• D. \( 0 \)

Hint:

The phase difference between the flux and the induced e.m.f. in a rotating coil is \( \frac{\pi}{2} \) because the rate of change of flux is proportional to the sine of the angle, while flux itself varies with the cosine of the angle.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Induced emf is the rate of change of magnetic flux. In a rotating coil, the flux varies sinusoidally, and its derivative (emf) will have a different phase.
Step 2: Key Formula or Approach:
1. Flux \( \phi = NBA \cos(\omega t) \).
2. emf \( e = -\frac{d\phi}{dt} = NBA\omega \sin(\omega t) \).
Step 3: Detailed Explanation:
The flux follows a cosine function: \( \phi \propto \cos(\omega t) \).
The induced emf follows a sine function: \( e \propto \sin(\omega t) \).
We know that \( \sin(\theta) = \cos(\theta - \pi/2) \).
The phase difference between a sine and cosine function of the same frequency is \( 90^\circ \) or \( \pi/2 \).
Step 4: Final Answer:
The phase difference is \( \pi/2 \).