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(D) Given: Radius $r = 10\, cm = 0.1\, m$,Magnetic field $B = 3.0 	imes 10^{-5}\, T$.Time for half rotation is $0.2\, s$,so the time period $T = 0.4\

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$15$

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(D) Given: Radius $r = 10\, cm = 0.1\, m$,Magnetic field $B = 3.0 	imes 10^{-5}\, T$.Time for half rotation is $0.2\, s$,so the time period $T = 0.4\, s$.The magnetic flux through the coil at any time $t$ is $\phi = BA \cos(\omega t)$,where $A = \pi r^2$ is the area of the coil.The induced $EMF$ is given by Faraday's law: $|\varepsilon| = |\frac{d\phi}{dt}| = |BA\omega \sin(\omega t)|$.The maximum induced $EMF$ is $\varepsilon_{\max} = BA\omega$.Substituting $\omega = \frac{2\pi}{T}$:$\varepsilon_{\max} = B 	imes (\pi r^2) 	imes \frac{2\pi}{T} = \frac{2\pi^2 B r^2}{T}$.Substituting the values: $\varepsilon_{\max} = \frac{2 	imes \pi^2 	imes 3.0 	imes 10^{-5} 	imes (0.1)^2}{0.4}$.Using $\pi^2 \approx 10$:$\varepsilon_{\max} = \frac{2 	imes 10 	imes 3.0 	imes 10^{-5} 	imes 0.01}{0.4} = \frac{6 	imes 10^{-4}}{0.4} = 15 	imes 10^{-6}\, V = 15\, \mu V$.

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