Say I have a single turn of a coil in an external magnetic field. How do I calculate the voltage induced in this turn ? Initially I would use Faraday's law
∇×E = -j ω B
But what should I use for B ? Will B not be a combination of both the external field as well as the field created by the current induced in the coil:
∇×B = μ J = μ σ E
Suddenly the problem seems more complicated!