Question

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced

• A. Once per revolution
• B. Twice per revolution
• C. Four times per revolution
• D. Six times per revolution

Answer 1

The Correct Option is B

To solve the problem, we need to understand the phenomenon of electromagnetic induction in a rotating wire loop placed in a magnetic field. The induced electromotive force (EMF) in the loop is governed by Faraday's law of electromagnetic induction, which states that the induced EMF is proportional to the rate of change of magnetic flux through the loop.

The EMF can be expressed as:

E = -\frac{d\phi}{dt}

where \phi is the magnetic flux.

When a wire loop is rotated in a uniform magnetic field, the magnetic flux changes as a function of the angle of rotation. The flux 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 loop.

As the loop rotates through 360°, the direction of the magnetic flux relative to the loop changes, inducing an EMF. Every 180° of rotation, the direction of the magnetic flux changes, causing a change in the direction of the induced current. Therefore, the direction of the induced EMF (and hence the direction of the current) changes twice per revolution.

Let's analyze each option:

• Once per revolution: Incorrect. The direction changes each time the loop's plane is perpendicular to the magnetic field (twice per revolution).
• Twice per revolution: Correct. As explained, the direction of the induced EMF changes every 180° of rotation.
• Four times per revolution: Incorrect. This option would imply changes every 90°, which is not the case.
• Six times per revolution: Incorrect. There is no basis for a change of direction six times per revolution.

Therefore, the correct answer is that the direction of the induced EMF changes twice per revolution.