The General Form of Faraday's Law

A changing flux induces an emf, or potential difference, in a loop. Whenever we have a potential difference we have an electric field. If the potential difference is the induced emf, we get:

ε = E ds

The integral should be carried out over a closed loop so we can bring in the changing flux in that loop:

ε = -dΦB/dt

This gives, integrating around a closed loop, the general form of Faraday's Law:

E ds = -dΦB/dt

Electric fields produced by changing magnetic fields have some interesting properties: