Question

A wire loop is rotated in magnetic field. The frequency of change of direction of the induced e.m.f. is :

• A. Six times per revolution
• B. Once per revolution
• C. twice per revolution
• D. four times per revolution

Answer 1

The Correct Option is C

To determine the frequency of change of direction of the induced electromotive force (e.m.f) when a wire loop is rotated in a magnetic field, we need to understand the principles of electromagnetic induction.

1. The phenomenon of electromagnetic induction involves a change in magnetic flux linked with a circuit that induces an e.m.f in the circuit. According to Faraday's Law of Electromagnetic Induction, the induced e.m.f is given by:

   \(\text{e.m.f} = -\frac{d\Phi}{dt}\)

   where \(\Phi\) is the magnetic flux through the loop.

2. For a loop rotating in a uniform magnetic field, the magnetic flux \(\Phi\) is given by:

   \(\Phi = B \cdot A \cdot \cos(\theta)\)

   where \(B\) is the magnetic field strength, \(A\) is the area of the loop, and \(\theta\) is the angle between the magnetic field and the normal to the plane of the loop.

3. As the loop rotates, \(\theta\) changes with time. The e.m.f becomes alternating, changing direction whenever the derivative of cosine changes its sign. This occurs when \(\theta\) changes by \(\pi/2\), i.e., at every quarter of the revolution.

4. In one full revolution (360 degrees or \(2\pi\) radians), the e.m.f. will change its direction twice – once when \(\theta\) goes from \(\pi/2\) to \((3\pi/2)\) and once when it returns from \((3\pi/2)\) to \((5\pi/2)\).

5. Thus, the frequency of change of direction of the induced e.m.f. is twice per revolution.

Therefore, the correct answer is: twice per revolution.