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In a region of uniform magnetic induction B = 10^–2 tesla, a circular coil of radius 30 cm and resistance $π^{2} ohm$ is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is ___ mA.

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Detailed Solution

The induced emf generated in the coil due to its rotation in magnetic field is given by:

$\begin{array}{l} e = BANωsin ω t \\ \Rightarrow iR = BAN ω \sin ω t \Rightarrow i = \frac{BAN ω \sin ω t}{R} \\ \Rightarrow A m p l i t u d e o f c u r r e n t = \frac{(10^{- 2}) \times π \times 0 . 3^{2} \times 1 \times 200 \times 2 π}{π^{2} \times 60} A \\ \Rightarrow i = 6 mA \end{array}$

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