A uniform magnetic field B exists in a cylind | vedclass

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Question

(A) The side length of the square frame is $L = 80\,cm / 4 = 20\,cm = 0.2\,m$.The magnetic field is restricted to a circular region of radius $r = 10\

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The side length of the square frame is $L = 80\,cm / 4 = 20\,cm = 0.2\,m$.The magnetic field is restricted to a circular region of radius $r = 10\,cm = 0.1\,m$.The square frame is placed such that one side lies on the diameter. This means exactly half of the circular region lies within the square frame.The area of the magnetic field region inside the frame is $A = \frac{1}{2} \pi r^2 = \frac{1}{2} 	imes \pi 	imes (0.1)^2 = 0.005\pi\,m^2$.The induced electromotive force $(EMF)$ is given by Faraday's law: $e = \left| \frac{d\phi}{dt} ight| = A \frac{dB}{dt}$.Given $\frac{dB}{dt} = 0.010\,T/s$,we have $e = (0.005\pi) 	imes 0.010 = 5\pi 	imes 10^{-5}\,V$.The induced current is $i = \frac{e}{R} = \frac{5\pi 	imes 10^{-5}}{4.0} \approx \frac{5 	imes 3.1416 	imes 10^{-5}}{4} \approx 3.927 	imes 10^{-5}\,A$.Rounding to two significant figures,$i = 3.9 	imes 10^{-5}\,A$.

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