Question

A circular coil of area 200 cm\(^2\) and 50 turns is rotating about its vertical diameter with an angular speed of 40 rad/s in a uniform horizontal magnetic field of magnitude \(2 \times 10^{-2} \, \text{T}\). The maximum emf induced in the coil is.

• A. \( 1.2 \, \text{V} \)
• B. \( 0.8 \, \text{V} \)
• C. \( 0.6 \, \text{V} \)
• D. \( 0.3 \, \text{V} \)

Hint:

To calculate the maximum induced emf, multiply the number of turns, magnetic field, area, and angular speed.

Answer 1

The Correct Option is B

Step 1: The formula for the maximum induced emf in a rotating coil in a magnetic field is given by: \[ \mathcal{E}_{\text{max}} = N B A \omega \] where: - \( N = 50 \) (number of turns) - \( B = 2 \times 10^{-2} \, \text{T} \) (magnetic field) - \( A = 200 \, \text{cm}^2 = 200 \times 10^{-4} \, \text{m}^2 \) (area of the coil) - \( \omega = 40 \, \text{rad/s} \) (angular speed) 

Step 2: Substituting the values into the equation: \[ \mathcal{E}_{\text{max}} = 50 \times (2 \times 10^{-2}) \times (200 \times 10^{-4}) \times 40 \] \[ \mathcal{E}_{\text{max}} = 50 \times 2 \times 10^{-2} \times 200 \times 10^{-4} \times 40 \] \[ \mathcal{E}_{\text{max}} = 0.8 \, \text{V} \] Thus, the maximum emf induced in the coil is \( \boxed{0.8 \, \text{V}} \).