22. A big circular coil of 100 turns and average radius $10 m$ is rotating about its horizontal diameter at $2 rad s^{-1}$. If the vertical component of earth's magnetic field at that place is $2 \times 10^{-5} T$ and electrical resistance of the coil is $12.56 \Omega$, then the maximum induced current in the coil will be : (2022)
Solution:
The peak induced emf is given by $e_0 = N B A \omega = N B (\pi r^2) \omega$.
Substituting the values: $e_0 = 100 \times (2 \times 10^{-5}) \times (\pi \times 10^2) \times 2 = 4\pi \approx 12.56 V$.
The maximum induced current is $I_0 = \frac{e_0}{R} = \frac{12.56}{12.56} = 1 A$.
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