A uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4\ \text{mm}$ and a total length of $30\ \text{cm}$. The magnetic field changes with time at a steady rate $dB/dt = 0.032\ \text{T s}^{-1}$. The induced current in the loop is close to (Resistivity of the metal wire is $1.23\times10^{-8}\ \Omega\,\text{m}$)
Answer: (B) $0.61\ \text{A}$
Side of the square $= 7.5$ cm, so area $= (0.075)^{2} = 5.625\times10^{-3}\ \text{m}^{2}$ and $\varepsilon = 0.032\times5.625\times10^{-3} = 1.8\times10^{-4}$ V.
Resistance: $R = \dfrac{\rho l}{\pi r^{2}} = \dfrac{1.23\times10^{-8}\times0.3}{\pi(2\times10^{-3})^{2}} \approx 2.94\times10^{-4}\ \Omega$.
$$I = \frac{1.8\times10^{-4}}{2.94\times10^{-4}} \approx 0.61\ \text{A}$$
Solution by Sreeraj P, M.Sc Physics