Note on Faraday's law and Maxwell's equations

Abstract

We generalize the approach developed by us for the evaluation of the total time derivative of circular integral (Kholmetskii A L et al 2008 Eur. J. Phys. 29 L1-4) and derive an explicit expression for the total time derivative of the area integral for a differentiable vector field. On the basis of this expression, we prove for the first time that Faraday's law can be directly obtained from the Maxwell equations del x E = -delta B/delta t, del center dot B = 0 and the Lorentz force law.