Quote by MS La Moreaux
anirudh215,
In your reference it states, under "In electromagnetism," "Caution must be taken to avoid cases with moving boundaries: the partial time derivatives are intended to exclude such cases."
Mike

Please look up how
[tex] \epsilon = \frac{d \phi}{dt}[/tex]
is derived from Maxwell's equations. I too have the read the Feynman lectures and I strongly feel that was not what Feynman tried to convey. Feynman disagrees that
[tex] \epsilon = \frac{d \phi}{dt}[/tex]
includes all cases. That is true. It does not include all cases. The most popular example to show that it does not include all cases is the example that you yourself have stated. In such a case, the path of the current is itself not clear and applying the above law does not hold good. The above law is NOT Faraday's law. I have already stated Faraday's law above. When using the law that I have stated, indeed, the integral IS done around a stationary path.
Why don't you take up some standard text like Griffiths'
Introduction to Electromagnetism or Schwartz's
Principles of Electrodynamics and look this up? It is quite lucidly explained. The vxB part is definitely included in the flux rule which you have stated above.