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(A) According to Faraday's Law of electromagnetic induction,the induced electromotive force $(EMF)$ $\varepsilon$ is given by the negative rate of cha

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$0.5$

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(A) According to Faraday's Law of electromagnetic induction,the induced electromotive force $(EMF)$ $\varepsilon$ is given by the negative rate of change of magnetic flux: $\varepsilon = -\frac{d\phi}{dt}$.Given $\phi = 50t^2 + 4$,we differentiate with respect to $t$:$\frac{d\phi}{dt} = \frac{d}{dt}(50t^2 + 4) = 100t$.Thus,the magnitude of the induced $EMF$ is $|\varepsilon| = 100t$.At time $t = 2 \ s$,the induced $EMF$ is $|\varepsilon| = 100(2) = 200 \ V$.The current $I$ in the coil is given by Ohm's Law: $I = \frac{|\varepsilon|}{R}$.Given resistance $R = 400 \ \Omega$,we have $I = \frac{200}{400} = 0.5 \ A$.

$A$ 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 $t = 2 \ s$ will be: (in $A$)

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