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A uniform magnetic field B exists in a cylindrical region of radius 10cm as shown in figure. A uniform wire of length 80 cm and resistance 4.0 $Ω$ is bent into a square frame and is place with one side along a diameter of the cylindrical region, If the magnetic field increases at a constant rate of $0 .010 T / s,$ find the current induced in the frame. $(in μA)$

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answer is 39.26.

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Detailed Solution

Flux in the frame: $ϕ = BA = B \frac{{πr}^{2}}{2}$

Induced current: $i = \frac{1}{R} \frac{dϕ}{dt} = \frac{1}{R} \frac{{πr}^{2}}{2} \frac{dB}{dt}$
$= \frac{1}{4} \times \frac{3 .14 \times 10^{- 2}}{2} \times 0 .01 = 39.26 μA$

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