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[en] 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 ∇ x E = -∂B/∂t, ∇ . B = 0 and the Lorentz force law. (note)
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