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(A) Given: Resistance $R = 400 \,\Omega$,Magnetic flux $\phi = 50t^2 + 4 \,Wb$.According to Faraday's law of electromagnetic induction,the induced ele

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(A) Given: Resistance $R = 400 \,\Omega$,Magnetic flux $\phi = 50t^2 + 4 \,Wb$.According to Faraday's law of electromagnetic induction,the induced electromotive force $(emf)$ is given by $\varepsilon = -\frac{d\phi}{dt}$.$\varepsilon = -\frac{d}{dt}(50t^2 + 4) = -100t \,V$.At time $t = 2 \,s$,the magnitude of the induced $emf$ is $|\varepsilon| = |-100(2)| = 200 \,V$.The induced current $I$ in the coil is given by Ohm's law: $I = \frac{|\varepsilon|}{R}$.$I = \frac{200 \,V}{400 \,\Omega} = 0.5 \,A$.

$A$ coil of resistance $400 \,\Omega$ is placed in a magnetic field. If the magnetic flux $\phi \,(Wb)$ linked with the coil varies with time $t \,(s)$ as $\phi = 50t^2 + 4$,the current in the coil at $t = 2 \,s$ is.....$A$.

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