content(warnings): Add W17-W28, X8-X12, N7 — E&M misconceptions, cross-refs, notes

concepts/em/u13/e13-3-lenz.tex

@@ -20,10 +20,14 @@ The operational procedure is:
 \item Use the right-hand rule on $\vec{B}_{\text{ind}}$ to find the induced current direction: curl the fingers of your right hand in the current direction; your thumb points along $\vec{B}_{\text{ind}}$.
 \end{enumerate}}
 
+\wc{Lenz's law opposes the \emph{change} in flux, not the field itself}{The induced current creates a field that opposes the \emph{change} in magnetic flux, not the external field itself. If flux is \emph{increasing}, the induced field opposes the external field. If flux is \emph{decreasing}, the induced field is in the \emph{same} direction as the external field (to try to maintain it).}
+
 \nt{The negative sign in Faraday's law \emph{is} Lenz's law written as an equation. If the sign were positive, the induced current would reinforce the flux change, producing more flux in the same direction, which would drive yet more current --- an energy-creating runaway. Lenz's law prevents this by ensuring the induced field opposes the change.}
 
 \thm{Lenz's law (energy-conservation form)}{The direction of induced current in any closed loop is always such that the magnetic force or torque on the loop opposes the motion or change that produced the induction. Equivalently, mechanical work must be done against the magnetic forces to sustain the change in flux; this work is converted to electrical energy (and ultimately to thermal energy in the resistance of the loop).}
 
+Lenz's law is the directional consequence of Faraday's law (Section 13.2) and is deeply connected to energy conservation. The same principle governs motional EMF in Section 13.4 and inductance in Section 13.5.
+
 \pf{Lenz's law from energy conservation}{Suppose a magnet is pushed toward a conducting loop. The induced current creates a magnetic field $\vec{B}_{\text{ind}}$ that opposes the approaching magnet. An external agent must do positive work against the magnetic repulsion to keep the magnet moving. This work supplies the electrical energy dissipated as Joule heating in the loop.
 
 If Lenz's law were reversed --- if the induced field \emph{aided} the approaching magnet --- the magnet would accelerate toward the loop without any external work, increasing both the kinetic energy of the magnet and the electrical energy dissipated in the loop, with no energy input. This violates conservation of energy. Therefore, the minus sign in Faraday's law is required by energy conservation. \Qed}