Question about induced current

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Say we have an induced circuit. My book states that we cannot use the loop rule on an induced circuit because we cannot define a potential difference in the circuit. If the potential difference is undefined how can current exist?

There's probably a really obvious answer, but I'm not seeing it.
 

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Say we have an induced circuit. My book states that we cannot use the loop rule on an induced circuit because we cannot define a potential difference in the circuit. If the potential difference is undefined how can current exist?

There's probably a really obvious answer, but I'm not seeing it.
The potential is defined as long as a path is specified. In electric fields due to charged particles with no time-changing magnetic fields present, the potential from a to b is well defined as it is independent of the path of integration. This electric field is called conservative, and it has no "curl, aka rotation or circulation".

When ac magnetic fields are present there must also be an electric field present. This E field is non-consevative, and has "curl", or rotation, circulation if you prefer. The potential is the line integral around the loop, and is path dependent. A path which encloses a larger area encloses a larger magnetic flux, in webers, and the potential is larger.

If a closed loop having resistance R is subjected to an ac magnetic field, current will be induced. The potential around the loop is defined as long as a specific path is considered. Ohm's law is always upheld so that the voltage around the loop divided by the current always equals R. The potential is the work done per unit charge transporting the charge around the loop *along a specific path*. Again if no ac magnetic fields were present the potential around a closed loop equals zero independent of path taken. Kirchoff's voltage law is a special case of Faraday's law.

If this gives you trouble at first, don't feel bad. Great minds struggle with induction. I know degreed EE's practicing for decades who still have only a partial understanding of induction. Have I answered your question? BR.

Claude
 
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