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

concepts/em/u12/e12-2-particle-motion-in-b.tex

@@ -72,6 +72,8 @@ The sense of the circular rotation follows the same rule as cyclotron motion: co
 
 \nt{If $\alpha=0^\circ$, then $v_{\perp}=0$ and the particle travels in a straight line along $\vec{B}$ (no magnetic force). If $\alpha=90^\circ$, then $v_{\parallel}=0$ and the particle undergoes pure circular motion (no drift along $\vec{B}$). Helical motion interpolates between these two extremes. The pitch increases as $\alpha\to 0^\circ$ and approaches zero as $\alpha\to 90^\circ$.}
 
+\wc{Field lines are a visualization tool, not physical threads}{Magnetic field lines are a mathematical construct to visualize $\vec{B}$. The field is continuous and exists at every point --- field lines are just a convenient drawing. Charges do not follow field lines (except when $\vec{v}\parallel\vec{B}$). The density of lines indicates field strength, but the lines themselves have no physical substance.}
+
 \mprop{Cyclotron and helical motion parameters}{For a particle of mass $m$ and charge $q$ in a uniform magnetic field $\vec{B}$, with velocity $\vec{v}$ at angle $\alpha$ to $\vec{B}$:
 \begin{align}
 R&=\frac{m\,v\,\sin\alpha}{|q|\,B} && \text{(helix radius)} \\