wuphysics87 @wuphysics87@qoto.org
@freemo Faraday's Law is cool :D
@freemo The feedback is a conceptualization of the way you couple the inductors together. Changing magnetic flux induces current. Which in turn produces a magnetic field from the current that is induced. Which is seen as a changing magnetic flux by the inductor producing the original magnetic field. The point is a matter of the interpretation of how you apply Faraday's Law and what your "choice" is when applying sign convention. One choice violates conservation of energy. Which makes it incorrect. The other results in the scaling relationship that you saw in your calculation.
@freemo Another way you could look at this is on the basis of conservation of energy in the context of Faraday's law. Consider the following thought experiment: two inductors are nested within one another with one connected to a battery, and the other forming a closed loop. The switch on the first is closed inducing a magnetic field in the second. A sort of "cascade" effect occurs when you think about this in terms of Faraday's Law. The first coil produces a magnetic field, but it does not experience an external one at the instant of closing the switch. The second in turn will experience an external magnetic field from the first, but also an induced magnetic field due to the current induced by the external field. This splitting is built into Faraday's Law. Faraday's Law doesn't care which magnetic field is which, just that there is a total magnetic field. Ultimately, the induced component must be smaller than the external component and opposite in direction. If it was larger, then the response in the next "time step" to the first coil would have an increase in current in the direction that was creating the original magnetic field. This would cascade to infinite current in both inductors and clearly conservation of energy is violated. Analogously you could consider the two coils like paddles in pong where either the choice is that the bounce the ball back and forth dampening and slowing it with each collision, or they swing harder and harder giving the ball an infinite velocity. As a result, your flux linking ratio MUST be less than 1. Otherwise energy conservation is violated. All of this is a consequence of Lenz's "Law" or the notion of "nature abhorring changes in flux" but really is embedded into Faraday's law via the negative sign and careful adherence to sign conventions when applying the right hand rule.
