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(A) The magnetic flux $\phi$ through the loop is given by $\phi = \vec{B} \cdot \vec{A}$.Given, area vector $\vec{A} = (10 	imes 10^{-4} \,m^2) \hat{

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$0.10$

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(A) The magnetic flux $\phi$ through the loop is given by $\phi = \vec{B} \cdot \vec{A}$.Given, area vector $\vec{A} = (10 	imes 10^{-4} \,m^2) \hat{k}$.The magnetic field vector $\vec{B} = B \hat{n}$, where $\hat{n}$ is the unit vector in the direction $\hat{i}+\hat{j}+\hat{k}$.Thus, $\vec{B} = 1.73 	imes \frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}} \,T$.Initial flux $\phi_i = \vec{B} \cdot \vec{A} = \left( \frac{1.73}{\sqrt{3}} (\hat{i}+\hat{j}+\hat{k}) ight) \cdot (10^{-3} \hat{k}) = \frac{1.73}{\sqrt{3}} 	imes 10^{-3} \,Wb$.Since $\sqrt{3} \approx 1.732$, $\phi_i \approx 10^{-3} \,Wb$.Final flux $\phi_f = 0$ as the field decreases to zero.The induced emf is $|e| = \left| -\frac{\Delta \phi}{\Delta t} ight| = \frac{\phi_i - \phi_f}{\Delta t} = \frac{10^{-3} \,Wb - 0}{10 \,s} = 10^{-4} \,V = 0.1 \,mV$.

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