Talk:Aromatic ring current

message: The picture has a major bug violating the right hand rule concerning induced electric current direction.
Lysanderos (talk) 22:14, 6 December 2009 (UTC)
thread_title: Untitled

message: Substituted at 08:17, 29 April 2016 (UTC)
thread_title: Assessment comment

message: Ampère's Law describes the magnetic field generated by current in a loop (cause: constant current, effect: constant magnetic field).  In contradiction to the opening remarks in this "Aromatic Ring Current" article, Ampère's Law does not describe currents in a loop that get generated by an external magnetic field.  That is Faraday's Law (cause: changing magnetic field, effect: changing electric field).  Faraday's Law relates the change in magnetic flux through a loop to the energy a unit charge would gain while going around the loop completely.
Example: Take a planar loop of wire (macroscopic and with finite resistance) and put it in a constant magnetic field perpendicular to the loop, say due to a permanent magnet.  Wait for transient effects to die down (a steady state).  There will be no current in the wire so Ampère's Law predicts it will generate no magnetic field.  The constant magnetic field due to the permanent magnet will not be zero, however.
Even when the aromatic sample is at equilibrium with its environment, the electrodynamic behaviour of a molecule is far from static.  However we can consider what net changes occur as a result of applying an external field for NMR measurement.  In addition to a strong oscillating field, the NMR apparatus has the sample spinning, and a secondary field is being swept through a range of frequencies, complicating analysis.  However we consider a time short enough so that the component of the driving magnetic field vertical to the plane of the aromatic ring is well-approximated by B0sin ωt (with B0 and ω constant), but long enough for the response to have synchronized.  
In this idealization, the magnetic flux through the aromatic ring is A ⋅  B0sin ωt, where A is the area of the ring, roughly constant.  The change in the flux is ∂/∂t (A ⋅ B0sin ωt) ≈ A ⋅  B0ωcos ωt.  The change induces a circular electric field in the π cloud according to Faraday's Law.  
The resulting additional motion of the charges in turn induces a magnetic field.  Although Ampère's Law, in its original form, technically applies only to constant currents in macroscopic wires, if we consider this additional motion of the charges in the π cloud, during a very short time, as a current, we can consider the induced magnetic field Ampère's Law would imply. Inside the area of the ring it would oppose the driving one, and outside the ring (in the same plane) it would be aligned with the driving one.  The circulation of the π electrons appears unimpeded, leading to the expectation of a large effect. Thus protons inside the ring are expected to be significantly "shielded" from the driving magnetic field, whereas the protons outside the ring are expected to be "deshielded."
While this analysis is suggestive, it is not expected to truthfully or quantitatively model the situation.  Describing the motion of the electrons and the fields they generate requires quantum mechanics.  — Preceding unsigned comment added by 50.66.189.2 (talk) 01:20, 22 January 2017 (UTC)
thread_title:  Ampère's law