Faraday Paradox - Inapplicability of Faraday's Law

Inapplicability of Faraday's Law

Figure 4 shows a translating rectangle of material with a narrow conducting strip subject to a magnetic field. This strip of material is rendered conducting at a fixed location by, for example, a strong light beam at this location. The magnetic field also is confined to the same strip. The Lorentz force drives a current from the top rail to the bottom rail through this strip, and the circuit is completed through leads attached to the top and bottom conducting rails. In this example, the circuit does not move, and the magnetic flux through the circuit is not changing, so Faraday's law suggests no current flows. However, the Lorentz force law suggests a current does flow. This example is based upon one devised by Richard Feynman to illustrate the inapplicability of Faraday's law of induction to certain situations (that is, the version of Faraday's law of induction which relates EMF to magnetic flux, which he terms the "flux rule"). Referring to his example, Feynman said:

The "flux rule" does not work in this case. It must be applied to circuits in which the material of the circuit remains the same. When the material of the circuit is changing, we must return to the basic laws. The correct physics is always given by the two basic laws

— Richard P Feynman  The Feynman Lectures on Physics

Accordingly, he explains the phenomenon using the Lorentz force law, as described above. The point is that the flux law applies only to some situations, albeit some very practical ones.