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Question

(B) The magnetic flux $\phi$ through the coil rotating in a magnetic field is given by $\phi = NBA \cos(\omega t)$.The induced electromotive force $(E

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$1$

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(B) The magnetic flux $\phi$ through the coil rotating in a magnetic field is given by $\phi = NBA \cos(\omega t)$.The induced electromotive force $(EMF)$ is $E = -\frac{d\phi}{dt} = NBA\omega \sin(\omega t)$.The maximum $EMF$ is $E_{\max} = NBA\omega$.The maximum induced current is $i_{\max} = \frac{E_{\max}}{R} = \frac{NBA\omega}{R}$.Given: $N = 1000$,$B = 2 	imes 10^{-5} \, T$,$r = 10 \, m$,$\omega = 2 \, rad \cdot s^{-1}$,$R = 12.56 \, \Omega$.Area $A = \pi r^2 = \pi (10)^2 = 100\pi \, m^2$.Substituting the values:$i_{\max} = \frac{1000 	imes (2 	imes 10^{-5}) 	imes (100\pi) 	imes 2}{12.56}$.Since $100\pi \approx 314$,$i_{\max} = \frac{1000 	imes 2 	imes 10^{-5} 	imes 314 	imes 2}{12.56} = \frac{12.56}{12.56} = 1 \, A$.

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