A circular coil of radius 10 cm, 500 turns and resistance 2 Omega is placed with its plane prependicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through `180^(@)` in 0.25 s. Estimate the magnitude of the e.m.f and current induced in the coil. Horizotal component of earth's magnetic field at the place is `3 xx 10^(-5) T`.

Explanation

To solve the problem step by step, we will use the formula for the induced electromotive force (e.m.f) in a coil when it is rotated in a magnetic field.

### Step 1: Identify the given values
- Radius of the coil (r) = 10 cm = 0.1 m
- Number of turns (N) = 500
- Resistance of the coil (R) = 2 Ω
- Horizontal component of the Earth's magnetic field (B) = \(3 \times 10^{-5}\) T
- Angle of rotation (θ) = 180° = π radians
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