A cylindrical region of radius \(R\) contains a spatially uniform magnetic field directed out of the page with magnitude changing at a constant rate \(\dfrac{dB}{dt} = \beta > 0\). Three closed paths, each enclosing the same area \(A\), lie entirely within the region: Path 1 is a circle centered on the magnetic field axis, Path 2 is a circle centered a distance \(d\) (where \(0 < d < R/2\)) from the axis, and Path 3 is an equilateral triangle. If \(\mathcal{E}_1\), \(\mathcal{E}_2\), and \(\mathcal{E}_3\) are the magnitudes of the induced electromotive force around paths 1, 2, and 3, and \(E_{\text{max},1}\) and \(E_{\text{max},2}\) are the maximum magnitudes of the induced electric field along paths 1 and 2, which of the following correctly compares these quantities?