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

concepts/em/u13/e13-2-faraday.tex

@@ -18,6 +18,8 @@ where $d\vec{A}$ is the oriented area element (direction given by the right-hand
 \]
 The minus sign encodes Lenz's law: the induced current produces a magnetic field that opposes the change in flux that created it.}
 
+\wc{Faraday's law creates EMF, not necessarily current}{A changing magnetic flux induces an \emph{electromotive force} $\mathcal{E}=-d\Phi_B/dt$. Whether current flows depends on whether the loop is conducting and whether there is a complete circuit. A changing flux through an open loop or a broken ring creates EMF (a potential difference) but no current flows.}
+
 \pf{Derivation from Faraday's law}{
 The EMF is the work per unit charge by the induced non-conservative field: $\mathcal{E}=\oint_C\vec{E}\cdot d\vec{\ell}$. When the magnetic flux $\Phi_B=\int_S\vec{B}\cdot d\vec{A}$ through the loop changes in time, a non-conservative electric field is induced with non-zero circulation. Energy conservation requires this circulation to equal the rate of flux change (with the minus sign from Lenz's law):
 \[

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}

concepts/em/u13/e13-4-motional-emf.tex

@@ -100,6 +100,8 @@ Thus $P_{\text{mech}} = P_{\text{elec}}$, consistent with conservation of energy
 \]
 This is exactly the motional-emf result $\mathcal{E} = B\ell v$. Faraday's law provides the same emf through the ``flux-change'' perspective, while the motional-emf derivation provides it through the ``force-on-charges'' perspective.}
 
+The motional EMF $\mathcal{E}=B\ell v$ is consistent with Faraday's law $\mathcal{E}=-d\Phi_B/dt$ through the flux change perspective. Both derivations (force-on-charges and flux-change) appear in Sections 13.2 and 13.4 respectively and yield identical results.
+
 \ex{Illustrative example}{A metal rod of length $\ell$ rotates with angular speed $\omega$ about one end in a uniform magnetic field $B$ perpendicular to the plane of rotation. Different points on the rod have different speeds $v(r) = r\,\omega$, so the emf must be computed by integration:
 \[
 \mathcal{E} = \int_{0}^{\ell} B\,(r\omega)\,dr = \frac{1}{2}\,B\,\omega\,\ell^{2}.\]}

concepts/em/u13/e13-5-inductance.tex

@@ -12,6 +12,8 @@ Equivalently, from Faraday's law of induction, a changing current induces an EMF
 \]
 where the negative sign reflects Lenz's law: the induced EMF opposes the change in current. The SI unit of inductance is the henry (H), where $1\;\mathrm{H} = 1\;\mathrm{V\!\cdot\!s/A} = 1\;\mathrm{kg\!\cdot\!m^2/(s^2\!\cdot\!A^2)}$.}
 
+\wc{An inductor opposes \emph{change} in current, not current itself}{An ideal inductor with steady (DC) current has zero voltage drop across it ($V=0$ when $dI/dt=0$). It only produces a back-EMF $\mathcal{E}=-L(dI/dt)$ when the current is \emph{changing}. A steady current passes through an ideal inductor as freely as through a wire.}
+
 \nt{Inductance is purely a geometric property. For a fixed geometry (and no ferromagnetic material near the coil), $L$ is constant and independent of the current. The larger the coil, the more turns, and the greater the flux linkage per unit current, the larger the inductance. A coil with $L = 1\;\mathrm{H}$ and $dI/dt = 1\;\mathrm{A/s}$ develops a $1\;\mathrm{V}$ back EMF.}
 
 \thm{Solenoid self-inductance}{For an ideal long solenoid of length $\ell \gg R$, total turns $N$, cross-sectional area $A = \pi R^2$, and vacuum permeability $\mu_0 = 4\pi\times 10^{-7}\,\mathrm{T\!\cdot\!m/A}$, the magnetic field inside is $B = \mu_0\,n\,I$ where $n = N/\ell$. The flux through each turn is $\Phi_B = B\,A = \mu_0 N I A/\ell$. Therefore