I [find Lewis Little's] reply of May 04 to kt4ye [confusing, and I believe it may] be in error.
Faraday's law of induction correctly stated says that a current element J induces an E field (spherically) about itself according to the rate of change of that current. The direction of the E vector is identical with that of the current. If the current is increasing (positive derivative) then the E field (which has been termed the Electrokinetic E field for various reasons) is in the opposite direction to the current. Basically, the sign of the E field follows the negative of the sign of the derivative of the rate of change of current. It is that negative sign which constitutes Lenz's law. That makes Lenz's law a mathematical fact rather than a simple "rule of thumb".
Thus if one has a piece of wire with an increasing current, there is in space about that wire an E field directed oppositely to the current. That E field is also INSIDE the wire. There it cancels the E field that is trying to increase the current. This, then, tends to keep the current from increasing. This effect is well known and called inductance.
If a second wire loop lies near a first loop with increasing current, there will be an E field induced in that second loop in the opposite direction to the current in the first loop. This E field will try to induce a current in that second loop (which also has inductance) and will succeed to a degree in doing so. This current will be increasing and will be in the opposite direction to the first current. Since this second current is increasing it produces an E field back at the first wire in a direction opposite to it's source which is the second loop. And in this case that direction will be in the SAME direction as the original current. Hence the induced potential in the original wire will tend to INCREASE the current flow in that wire.
While this may seem to defy Lenz's law, it doesn't. The increasing current is actually due to some of the inductance of the first wire being canceled. In other words it's an effect like a shorted turn on a transformer or in another view, opposite currents in close-spaced wires create a non-inductive situation.
Hence in summary Lenz's law is due to the sign of the derivative of the current and when currents flow in opposite directions Lenz's law insures that the original current is increased rather than decreased due to cancellation of inductance.
Note that these arguments are made using classical Field theory and any questions of whether such fields are "real" or actually exist isn't considered here. The effects described by that model, however, clearly are real and exist.
I apologize for misunderstanding the initial post regarding Lenz's law.
[Mod: Probably referring to this one: viewtopic.php?f=6&t=8#p16 ]
The best manner in which to see how the Theory of Elementary Wave explains the generation of a current in one wire due to the change in the current in a neighboring wire is to imagine each wire as part of a very large loop. And, of course, each current would have to form a "loop" or there would be a buildup of charge somewhere. The analysis given in the book for Faraday's law then applies and explains the generation of current in the second "loop."
In my generation, Lenz's law wasn't taken as the law describing this effect, but was instead a "rule of thumb" to determine the direction in which an induced current would flow due to the change in another current. The induced current would itself change in a direction such as to generate an emf that would oppose the change to the initial current. I gather from the response to my initial post that the law is now understood as describing the overall process of induction. Of course, this "rule of thumb" assumes the validity of the laws governing induction.
Subject line changed to match post being replied to.
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Link to earlier post added.
Please note Moderator's Guideline @ guidelines/#selfcontained
Further notes regarding how Lenz's Law is and has been understood ...
Encyclopedia Britannica 1911 does not seem to have a separate entry for Lenz's Law.
However it is mentioned in two articles, as follows:
The creation of an external magnetic field H will, in accordance with Lenz's law, induce in the molecule an electric current so directed that the magnetization of the equivalent magnet is opposed to the direction of the field.
Now in the dynamo the active wires are placed so that their length is at right angles to the field; hence when they are rotated and an electric current begins to flow under the E.M.F. which they induce, a mutual force at once arises between the copper conductors and the magnet, and the direction of this force must by Lenz's law be opposed to the direction of the movement.
The current online Britannica (with limited access) has a separate entry for Lenz's Law, which begins like this:
http://www.britannica.com/EBchecked/top ... /Lenzs-law
in electromagnetism, statement that an induced electric current flows in a direction such that the current opposes the change that induced it. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz (1804–65).
From this site: http://www.physics247.com/physics-help/lenz-law.shtml
Definition of Lenz's Law
Lenz's Law is the observation that the current induced in a circuit flows in a direction that produces a magnetic field opposing the change in flux that produces the current.
The current Wikipedia entry introduces Lenz's Law as follows:
Lenz's law ... is an extension of the law of conservation of energy to the non-conservative forces in electromagnetic induction. It can be used to give the direction of the induced electromotive force (emf) and current resulting from electromagnetic induction. The law provides a physical interpretation of the choice of sign in Faraday's law of induction, indicating that the induced emf and the change in flux have opposite signs. Heinrich Lenz formulated the law in 1834.