# A uniform magnetic field $\inline B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $\inline 4\; mm$ and a total length of $\inline 30\; cm$. The magnetic field changes with time at a steady rate $dB/dt=0.032\; Ts^{-1}$. The induced current (in A) in the loop is close to (Resistivity of the metal wire is $\inline 1.23\times 10^{-8}\; \Omega m$ ). Option: 1 0.61 Option: 2 0.43 Option: 3 0.34 Option: 4 0.53

$\dpi{150} \begin{array}{l} \text { Area of loop }=l^{2} / 16 \\ \\ \varepsilon=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=\left(\frac{\mathrm{d} \mathrm{B}}{\mathrm{dt}}\right) \frac{\ell^{2}}{16} \\ \\ \mathrm{I}=\frac{\left(\frac{\mathrm{dB}}{\mathrm{dt}}\right) \frac{\ell^{2}}{16} \times \pi \mathrm{r}^{2}}{\rho \ell} \end{array}$

$\dpi{150} \dpi{150} \begin{array}{l} I=\frac{30}{4} \times \frac{30}{4} \times \frac{10^{-4} \times 0.032 \times 4 \times 10^{-6} \times \pi}{1.23 \times 10^{-8} \times 30 \times 10^{-2}} \\ \mathrm{I}=612.68 \times 10^{-3}=0.61 \mathrm{~A} \end{array}$

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