Consider an LC circuit,with inductance L = 0. | vedclass

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(A) The induced electromotive force $(emf)$ in the circuit due to the changing magnetic field is given by Faraday's law: $\varepsilon = -\frac{d\Phi}{

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$4$

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(A) The induced electromotive force $(emf)$ in the circuit due to the changing magnetic field is given by Faraday's law: $\varepsilon = -\frac{d\Phi}{dt} = -A \frac{dB}{dt}$.Given $A = 1 \ m^2$ and $\frac{dB}{dt} = \beta = 0.04 \ T \ s^{-1}$,the magnitude of the induced $emf$ is $\varepsilon = 1 	imes 0.04 = 0.04 \ V$.This $emf$ acts as a voltage source in the $LC$ circuit. The current in an $LC$ circuit oscillates as $I(t) = I_0 \sin(\omega t)$,where $\omega = \frac{1}{\sqrt{LC}}$.The maximum current $I_0$ in an $LC$ circuit driven by a constant $emf$ $\varepsilon$ is given by $I_0 = \varepsilon \sqrt{\frac{C}{L}}$.Substituting the values: $I_0 = 0.04 	imes \sqrt{\frac{10^{-3}}{0.1}} = 0.04 	imes \sqrt{10^{-2}} = 0.04 	imes 0.1 = 0.004 \ A$.Converting to milliamperes: $I_0 = 0.004 	imes 1000 \ mA = 4 \ mA$.

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