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A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s−1^{-1}. If the vertical component of earth's magnetic field at that place is 2×10−52 \times 10^{-5} T and electrical resistance of the coil is 12.56 Ω\Omega, then the maximum induced current in the coil will be

A

0.25 A

B

1.5 A

C

1 A

D

2 A

Step-by-Step Solution

The magnetic flux ϕ=NBAcos⁡(ωt)\phi = NBA \cos(\omega t). The induced EMF ε=−dϕdt=NBAωsin⁡(ωt)\varepsilon = -\frac{d\phi}{dt} = NBA\omega \sin(\omega t). The maximum EMF εmax=NBAω\varepsilon_{max} = NBA\omega. The maximum current imax=εmaxR=NBAωRi_{max} = \frac{\varepsilon_{max}}{R} = \frac{NBA\omega}{R}. Substituting values: imax=1000×2×10−5×π×(10)2×212.56=1000×2×10−5×3.14×100×212.56=12.5612.56=1 Ai_{max} = \frac{1000 \times 2 \times 10^{-5} \times \pi \times (10)^2 \times 2}{12.56} = \frac{1000 \times 2 \times 10^{-5} \times 3.14 \times 100 \times 2}{12.56} = \frac{12.56}{12.56} = 1 \text{ A}.

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