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(D) Given the magnetic field $B = 0.01 - 2t \, Tesla$.The rate of change of the magnetic field is $\frac{dB}{dt} = -2 \, Tesla/s$.The area of the loop

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$9$

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(D) Given the magnetic field $B = 0.01 - 2t \, Tesla$.The rate of change of the magnetic field is $\frac{dB}{dt} = -2 \, Tesla/s$.The area of the loop inside the magnetic field is $A_{eff} = \frac{1}{2} 	imes (1 \, m)^2 = 0.5 \, m^2$.The induced $emf$ $(e)$ is given by Faraday's law of induction: $e = -\frac{d\phi}{dt} = -\frac{d}{dt}(B \cdot A_{eff})$.$e = -A_{eff} \cdot \frac{dB}{dt} = -(0.5 \, m^2) 	imes (-2 \, Tesla/s) = 1 \, V$.Since the magnetic field is decreasing,the induced $emf$ acts in a direction that opposes the change. According to Lenz's law,the induced $emf$ will oppose the main battery $emf$ of $10 \, V$.Therefore,the resultant $emf = 10 \, V - 1 \, V = 9 \, V$.

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