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

concepts/em/u12/e12-1-magnetic-force-charge.tex

@@ -24,6 +24,8 @@ where $\theta$ is the angle between the vectors $\vec{v}$ and $\vec{B}$ measured
 \item \textbf{SI unit of $B$:} The tesla, $\mathrm{T} = \dfrac{\mathrm{N}}{\mathrm{C}\cdot\mathrm{m/s}} = \dfrac{\mathrm{N}}{\mathrm{A}\cdot\mathrm{m}} = \dfrac{\mathrm{kg}}{\mathrm{C}\cdot\mathrm{s}}$.
 \end{itemize}}
 
+The magnetic force on a single charge (this section) generalizes to the magnetic force on a current-carrying wire (Section 12.3) by summing over all charge carriers. The Biot-Savart law (Section 12.4) gives the reverse: how currents produce the $\vec{B}$ field that exerts these forces.
+
 \pf{Lorentz magnetic force law from cross-product geometry}{The vector cross product $\vec{v}\times\vec{B}$ is defined to have magnitude $vB\sin\theta$ and direction given by the right-hand rule. Multiplying by $q$ scales the magnitude by $|q|$ and reverses direction if $q<0$. Thus
 \[
 \vec{F}_B = q\,(\vec{v}\times\vec{B})
@@ -32,6 +34,8 @@ has magnitude $|q|vB\sin\theta$ and the correct directional behaviour. This is t
 
 \cor{Charge at rest or parallel to field}{When $\vec{v}=\vec{0}$ or when $\vec{v}\parallel\vec{B}$, we have $\sin\theta=0$ and therefore $F_B=0$. The magnetic field exerts no force on a stationary charge or on a charge moving exactly along the field lines.}
 
+\wc{A stationary charge produces zero magnetic field}{A point charge at rest produces only an \emph{electric} field. A magnetic field is produced only by \emph{moving} charges (currents) or changing electric fields (displacement current). A single stationary charge $q$ has $\vec{B}=\vec{0}$ everywhere.}
+
 \mprop{Magnetic force vs.\ electric force}{For the same charge $q$ placed in both an electric field $\vec{E}$ and a magnetic field $\vec{B}$, the total Lorentz force is
 \[
 \vec{F} = q\,\vec{E} + q\,\vec{v}\times\vec{B}.
@@ -49,6 +53,8 @@ P = \vec{F}_B\cdot\vec{v} = q\,(\vec{v}\times\vec{B})\cdot\vec{v} = 0.
 \]
 The magnetic force can change the direction of a particle's velocity but never its kinetic energy. This is the mathematical expression of the scalar triple-product identity $(\vec{a}\times\vec{b})\cdot\vec{a}=0$.}
 
+\wc{Magnetic force does zero work --- always}{Because $\vec{F}_B=q\vec{v}\times\vec{B}$ is always perpendicular to $\vec{v}$, the power $P=\vec{F}_B\cdot\vec{v}=0$. The magnetic force can change a particle's direction but never its speed or kinetic energy. Even in complex field configurations, the magnetic force contributes zero to the work integral $\int\vec{F}\cdot d\vec{r}$.}
+
 \ex{Illustrative example}{When a charged particle enters a uniform magnetic field perpendicularly, it follows a circular path. The magnetic force provides the centripetal force:
 \[
 |q|\,v\,B = \frac{m\,v^2}{R} \quad\Rightarrow\quad R = \frac{m\,v}{|q|\,B},