Faraday paradox
The Faraday paradox or Faraday's paradox is any experiment in which Michael Faraday's law of electromagnetic induction appears to predict an incorrect result. The paradoxes fall into two classes:
Faraday deduced his law of induction in 1831, after inventing the first electromagnetic generator or dynamo, but was never satisfied with his own explanation of the paradox.
Faraday's law (also known as the Faraday–Lenz law) states that the electromotive force (EMF) is given by the total derivative of the magnetic flux with respect to time t:
where is the EMF and ΦB is the magnetic flux. The direction of the electromotive force is given by Lenz's law. An often overlooked fact is that Faraday's law is based on the total derivative, not the partial derivative, of the magnetic flux. This means that an EMF may be generated even if total flux through the surface is constant. To overcome this issue, special techniques may be used. See below for the section on Use of special techniques with Faraday's law. However, the most common interpretation of Faraday's law is that:
This version of Faraday's law strictly holds only when the closed circuit is a loop of infinitely thin wire, and is invalid in other circumstances. It ignores the fact that Faraday's law is defined by the total, not partial, derivative of magnetic flux and also the fact that EMF is not necessarily confined to a closed path but may also have radial components as discussed below. A different version, the Maxwell–Faraday equation (discussed below), is valid in all circumstances, and when used in conjunction with the Lorentz force law it is consistent with correct application of Faraday's law.
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