HardPhysics
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A circular coil of wire consists of exactly 50 turns with a total resistance of 0.4 Ω. The area of the coil is 0.2 m². The coil is kept in a uniform magnetic field (B) as shown in figure. The magnetic field is decreased at a constant rate of 3 T/s. The induced current in the coil is
A
37.5 A
B
(37.5)√3 A
C
75 A
D
75√3 A
Explanation
Induced emf ε = -N * dΦ/dt = -N * A * cos(θ) * dB/dt. Here N=50, A=0.2, θ=30°, dB/dt = -3 T/s. ε = 50 * 0.2 * cos(30°) * 3 = 10 * (√3/2) * 3 = 15√3 V. Induced current I = ε/R = 15√3 / 0.4 = 37.5√3 A.
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