A circular coil of 100 turns and area of cross-section $10^{-2} m^2$ is rotated about its vertical diameter at 60 rpm in a uniform horizontal magnetic field of $3.5 × 10^{-2} T$. The maximum emf induced in the coil is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.22 V
Given:
Number of turns, $N = 100$
Area of coil, $A = 10^{-2}\ \text{m}^2$
Magnetic field, $B = 3.5 \times 10^{-2}\ \text{T}$
Rotation rate, $f = 60\ \text{rpm} = 1\ \text{rev/s}$
Angular frequency: $\omega = 2\pi f = 2\pi \times 1 = 2\pi\ \text{rad/s}$
Maximum emf in a rotating coil: $\mathcal{E}_\text{max} = N A B \omega$
Substitute values:
$\mathcal{E}_\text{max} = 100 \times 10^{-2} \times 3.5 \times 10^{-2} \times 2\pi$
$\mathcal{E}_\text{max} = 1 \times 3.5 \times 10^{-2} \times 2\pi = 0.035 \times 6.283 \approx 0.22\ \text{V}$
∴ Maximum induced emf = $0.22\ \text{V}$