I guess I'd like to revise my previous answer by allowing (as is, in fact,
regularly done) emf's to be defined for other than closed loops. It
certainly is possible to integrate along other than closed paths. The
only real advantage to closed paths is that the result is then directly
related to the rate of change of the enclosed magnetic flux. In the case
of a conducting loop with a gap, the integral from one side of the gap
around the loop to the other side would generally stay pretty close to
zero as long as the loop is a good conductor and the (almost) enclosed
flux isn't changing the rate at which its changing very quickly. (Did
that make sense?) This is the simple result of the build up of static
charges which would arrange themselves naturally to cancel any induced
electric fields. There could, of course, be a fairly intense electric
field across the gap and, possibly sparks. (Say, I'll bet you could use
that for something.)
John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
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