The concept of electromotive force (EMF) is typically used to describe the driving force behind the flow of electric charges in a closed circuit. While induced electric fields are indeed nonconservative fields, the concept of EMF can still be applied in the context of electromagnetic induction.
In the case of electromagnetic induction, a changing magnetic field induces an electric field, which in turn can drive the motion of charges within a conductor. This induced electric field is nonconservative because it does not satisfy the requirements of being a conservative field (i.e., having zero curl).
However, when a closed conducting loop is present within the region where the induced electric field exists, the nonconservative nature of the field does not prevent us from defining an EMF. The EMF is defined as the work done per unit charge in moving a charge around a closed loop, and it represents the total energy per unit charge that is supplied by the nonconservative electric field to overcome the resistance of the circuit.
Mathematically, the EMF can be calculated using Faraday's law of electromagnetic induction, which states that the EMF induced in a closed loop is equal to the negative rate of change of magnetic flux through the loop:
EMF = -dΦ/dt
Here, EMF represents the electromotive force, dΦ/dt represents the rate of change of magnetic flux, and the negative sign indicates the direction of the induced current.
In summary, even though the induced electric field is nonconservative, the concept of EMF can still be defined and used to describe the driving force behind the flow of charges in a closed circuit in the context of electromagnetic induction.