A flat, circular loop of radius \(r\) is placed in a uniform magnetic field such that the plane of the loop is perpendicular to the field lines. The magnetic field magnitude increases at a constant rate \(\left|\dfrac{\Delta B}{\Delta t}\right| = C\), inducing an electromotive force of magnitude \(\mathcal{E}_1\) in the loop. A second flat, circular loop has a radius of \(3r\) and is placed in a different uniform magnetic field whose magnitude increases at a constant rate \(\left|\dfrac{\Delta B}{\Delta t}\right| = 4C\). The second loop is oriented such that the normal to its plane makes an angle of \(60^\circ\) with the magnetic field lines. What is the ratio of the magnitude of the induced electromotive force in the second loop to that in the first loop, \(\dfrac{\mathcal{E}_2}{\mathcal{E}_1}\)?