Not necessarily. The electromotive force can also be due to a magnetic field, as in the case under consideration. The mere presence of an elecromotive force does not provide enough information to determine if it is an electric or a magnetic field or both. In the case under consideration it is due purely to the magnetic field, there is no electric field.The electric field is the electromotive force which would be on a unit charge at a given location if there is a charge present.
The notation is archaic, and I don't know what all the variables are, so I cannot comment much on that equation. However, only three variables could possibly be the components of the electric field, and there are more than three variables. So clearly, the mere fact of an electromotive force does not imply an electric field by that equation either.See #14 above.