The area vector of a rectangular loop that is initially \(\ell_{\mathrm{i}}=300 \mathrm{~mm}\) long and \(w_{\mathrm{i}}=200 \mathrm{~mm}\) wide is aligned with the direction of a uniform magnetic field that has initial magnitude \(B_{\mathrm{i}}=500 \mathrm{mT}\). You want to increase the field magnitude smoothly to \(B_{\mathrm{f}}=700 \mathrm{mT}\) in \(10 \mathrm{~s}\), but you want to have zero induced current in the loop. You plan to accomplish this by changing the loop's length \(\ell\) as you increase the magnetic field. In order to have \(I_{\text {ind }}=0\), what must the loop length be after \(3.00 \mathrm{~s}\) and after \(10.0 \mathrm{~s}\) ?