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(B) According to Faraday's law of electromagnetic induction,the induced electromotive force (emf) $\varepsilon$ is given by the rate of change of magn

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(B) According to Faraday's law of electromagnetic induction,the induced electromotive force (emf) $\varepsilon$ is given by the rate of change of magnetic flux: $\varepsilon = |\frac{d\phi}{dt}|$. Given $\phi(t) = 2t^2 + 2t + 1$,we differentiate with respect to $t$: $\varepsilon = |\frac{d}{dt}(2t^2 + 2t + 1)| = |4t + 2|$. At $t = 2 \ s$,the induced emf is: $\varepsilon = 4(2) + 2 = 10 \ V$. Using Ohm's law,the current $i$ is given by $i = \frac{\varepsilon}{R}$. Given resistance $R = 10 \ \Omega$,the current is: $i = \frac{10 \ V}{10 \ \Omega} = 1 \ A$.

Magnetic flux linked with the coil is given by $\phi(t) = 2t^2 + 2t + 1$ and its resistance is $10 \ \Omega$. The current passing through the coil at $t = 2 \ s$ is . . . . . . $A$.

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