To determine which law illustrates the relationship between induced electromotive force (EMF) and the time variation of magnetic flux in a coil, we need to understand the concepts of electromagnetic induction.

Let's examine the options:

• Ampere Circuital Law: This law relates the circulating magnetic field in a closed loop to the electric current passing through the loop. It does not directly deal with induced EMF or changes in magnetic flux.
• Faraday Law of Induction: This law states that the induced EMF in a closed circuit is equal to the negative rate of change of magnetic flux through the circuit. Mathematically, it is expressed as: E = -\dfrac{d\Phi}{dt}, where E is the induced EMF and \Phi is the magnetic flux. This directly illustrates the relationship between induced EMF and the time variation of magnetic flux.
• Lenz's Law: Lenz's Law gives the direction of induced current in a closed loop, stating that the direction is such that it opposes the change in magnetic flux that produced it. While related to electromagnetic induction, it does not describe the mathematical relationship of EMF and flux change itself.
• Coulomb's Law: This law describes the electrostatic force between charged particles, which is not related to electromagnetic induction or magnetic flux.

Thus, the correct answer is Faraday Law of Induction as it directly describes the relationship between induced EMF and the time rate of change of magnetic flux in a coil.

Conclusion: Faraday Law of Induction is the law that illustrates the relationship between induced electromotive force and time variation of magnetic flux in a coil, expressed as E = -\dfrac{d\Phi}{dt}.