A circular coil of 200 turns and mean radius 30 cm is placed in a uniform magnetic field of induction 0.02 T and is free to rotate about an axis coinciding with its own plane, but perpendicular to the uniform magnetic field. The coil is in closed circuit having a total resistance of `50 Omega`. if the plane of the coil is initially perpendicular to the field find the charge flown through the circuit, when the coil is rotated through (i) `60^@` (ii) `180^@` .

Explanation

To solve the problem, we need to calculate the charge that flows through the circuit when the coil is rotated through two angles: \(60^\circ\) and \(180^\circ\). We will use Faraday's law of electromagnetic induction to find the induced electromotive force (emf) and then use Ohm's law to find the charge.

### Given Data:
- Number of turns, \(N = 200\)
- Mean radius of the coil, \(r = 30 \text{ cm} = 0.3 \text{ m}\)
- Magnetic field induction, \(B = 0.02 \text{ T}\)
- Total resistance of the circuit, \(R = 50 \Omega\)

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