As most of us would know, the electric field in a material medium is dependent on the dielectric constant of the medium. Thus, the net electric field in the region shall depend on the properties of the medium itself.
Other than that, quantitatively the phenomena of electromagnetic induction is given by the Faraday's law as,
# E = - (dphi""_B)/dt# where #phi""_B# is the magnetic flux and E is the emf generated.
The generation of emf is due to the generation of the electric field.
In terms of Maxwell's equations, the phenomena can be described accurately as,
#nabla# X E = # -(delB)/(delt) # where B is the magnetic field.
Now that we know that flux change induces an electric field, it should be a matter of common sense that, the flux can be changed in several ways, by changing the magnitude of the field, the changing the area or my changing the orientation of the field with respect to the area.
The negative sign indicates that, emf is so produced that it tends to oppose the change in the field that produced it which is described by the Lenz law in accordance with the law of conservation of energy.
If flux change occurs within a closed circuit, the emf so produced shall produce a current in the circuit.
In absence of a closed circuit, the electric field (and the emf) is still there.