A square loop of side 10 cm and resistance \(0.5 \Omega\) is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set across the plane in the north-east direction. The magnetic field decreases to zero at 0.70 s at a steady rate. Then the magnitude of the induced current during this time interval will be __________.

A

\(\begin{array}{l} B =0.10 T \\ A =(10)^2 \\ A=100 cm^2 \\ R =0.5 \Omega\end{array}\)
Induced emf \(\varepsilon=-\frac{\Delta \phi_{ B }}{\Delta t}\)
\(\varepsilon=-\frac{\left(\phi_2-\phi_1 \cos 45^{\circ}\right)}{\Delta t}\)
\(\varepsilon=\frac{\phi_1 \cos 45^{\circ}}{\Delta t} \quad\left(\because \phi_2=0\right)\)
\(\varepsilon=\frac{ BA \cos 45^{\circ}}{\Delta t} \quad(\because \phi= BA )\)
\(\begin{array}{l}\varepsilon=\frac{0.1 \times 100 \times 10^{-4} \times 1}{0.70 \times \sqrt{2}} \\ \varepsilon=10^{-3} V\end{array}\)
Induced current \(I=\frac{\varepsilon}{R}\)
\(\begin{array}{l}I=\frac{10^{-3}}{0.5} \\ I=2 \times 10^{-3} A\end{array}\)