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Question:

A circular coil of radius 10 cm, 500 turns and resistance 2Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. If it is rotated about its vertical diameter through 180° in 0.25 s. The current induced in the coil is (Horizontal component of the earth's magnetic field at that place is 3.0 × 10⁻⁵ T).

1.9 × 10⁻⁷ A

2.9 × 10⁻⁷ A

4.9 × 10⁻⁷ A

3.9 × 10⁻⁷ A

Solution:

Initial magnetic flux through the coil, φ₁ = BHAcosθ = 3.0 × 10⁻⁵ × (π × 10⁻²) × cos0° = 3π × 10⁻⁷ Wb
Final magnetic flux after the rotation φf = 3.0 × 10⁻⁵ × (π × 10⁻²) × cos180° = -3π × 10⁻⁷ Wb.
Induced emf, ε = -Ndφ/dt = -N(φf - φi)/t = -( -3π × 10⁻⁷ - 3π × 10⁻⁷ )/0.25 = 500 × (6π × 10⁻⁷)/0.25 = 3.8 × 10⁻⁵ V
I = ε/R = 3.8 × 10⁻⁵ V/2Ω = 1.9 × 10⁻⁵ A.