Question

A metal disc of radius 100 cm is rotated at a constant angular speed of 60 rad/s in a plane at right angles to an external field of magnetic induction 0.5 Wb/m\(^2\). The emf induced between the centre and a point on the rim will be:

• A. 1.5 V
• B. 6 V
• C. 9 V
• D. 10 V

Hint:

The induced emf in a rotating conductor in a magnetic field is proportional to the angular velocity, magnetic field strength, and the square of the radius of the conductor.

Answer 1

The Correct Option is B

Step 1: The induced emf in a rotating disc is given by the formula: \[ \mathcal{E} = \dfrac{1}{2} B \omega r^2, \] where \( B \) is the magnetic field, \( \omega \) is the angular velocity, and \( r \) is the radius of the disc.
Step 2: Substituting the given values \( B = 0.5 \, \text{Wb/m}^2 \), \( \omega = 60 \, \text{rad/s} \), and \( r = 1 \, \text{m} \), we get: \[ \mathcal{E} = \dfrac{1}{2} \times 0.5 \times 60 \times 1^2 = 6 \, \text{V}. \]
Final Answer: \[ \boxed{6 \, \text{V}} \]