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Question:

A 800-turn coil of effective area 0.05 m² is kept perpendicular to a magnetic field 5 × 10⁻⁵ T. When the plane of the coil is rotated by 90° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be:

2V

0.2V

2 × 10⁻³V

0.02V

Solution:

Correct option is D. 0.02V
Magnetic field B = 5 × 10⁻⁵ T
Number of turns in coil N = 800
Area of coil A = 0.05 m²
Time taken to rotate Δt = 0.1 s
Initial angle θ₁ = 0°
Final angle θ₂ = 90°
change in magnetic flux ΔΦ = NBAcos90° − BAcos0° = −NBA = −800 × 5 × 10⁻⁵ × 0.05 = −2 × 10⁻³ weber
e = −ΔΦ/Δt = −(−2 × 10⁻³ Wb) / 0.1 s = 0.02V