Problem 3.305

A plane loop shown in Fig. 3.91 is shaped as two squares with sides \(a=20 \mathrm{~cm}\) and \(b=10 \mathrm{~cm}\) and is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as \(B=B_{0}\) sin \omegat, where \(B_{0}=10 \mathrm{mT}\) and \(\omega=100 \mathrm{~s}^{-1}\). Find the amplitude of the current induced in the loop if its resistance per unit length is equal to \(\rho=\) \(50 \mathrm{~m} \Omega / \mathrm{m} .\) The inductance of the loop is to be neglected.