A uniform magnetic field B exists in a cylind | vedclass

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(A) The side length of the square frame is $L = 80\, cm / 4 = 20\, cm = 0.2\, m$.The area of the square frame inside the magnetic field is the area of

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$3.9 	imes 10^{-5}\,A$

Vedclass · Answer

(A) The side length of the square frame is $L = 80\, cm / 4 = 20\, cm = 0.2\, m$.The area of the square frame inside the magnetic field is the area of a semicircle of radius $r = 10\, cm = 0.1\, m$.Area $A = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (0.1)^2 = 0.005\pi\, m^2$.The induced electromotive force $(EMF)$ is given by Faraday's law: $E_{	ext{ind}} = \frac{d\phi}{dt} = A \frac{dB}{dt}$.Given $\frac{dB}{dt} = 0.010\, T/s$,we have $E_{	ext{ind}} = (0.005\pi) 	imes 0.01 = 5 	imes 10^{-5} \pi\, V$.The induced current is $i = \frac{E_{	ext{ind}}}{R} = \frac{5 	imes 10^{-5} \pi}{4.0} = 1.25 	imes 10^{-5} \pi\, A$.Using $\pi \approx 3.14$,$i \approx 1.25 	imes 3.14 	imes 10^{-5} \approx 3.925 	imes 10^{-5}\, A$.Thus,the induced current is approximately $3.9 	imes 10^{-5}\, A$.

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