Faraday's Law and Ampere's Law

It is suggested that the origin of the induced electromotive force in a stationary circuit, given by Faraday's law of induction, could be made clearer to a beginning student if emphasis were placed in introductory courses on the geometry of the induced electric field set up by a time-varying magnetic field instead of on the line integral of this field around a closed path, or the emf in the path. If the Faraday law is written as $o∫E·ds = −Φ̇$⁠, instead of $ε = −Φ̇$⁠, it has the same form as Ampere's law, $o∫B·ds = μ0I$⁠, and both laws are simply the integral forms of the Maxwell equations, curl $E = −Ḃ$⁠, curl $H = J + Ḋ$⁠.