The current in a cylindrical solenoid is increased smoothly from \(I_{\mathrm{i}}=0.40 \mathrm{~A}\) at \(t_{\mathrm{i}}=3.0 \mathrm{~s}\) to \(I_{\mathrm{f}}=1.20 \mathrm{~A}\) at \(t_{\mathrm{f}}=5.0 \mathrm{~s}\). What is the induced emf during this time interval if the solenoid length is \(\ell=150 \mathrm{~mm}\), the radius of each winding is \(R=20 \mathrm{~mm}\), and there are 400 windings?