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

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2026-05-05 00:08:27 -05:00
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@@ -8,6 +8,8 @@ This subsection defines the electric field from source charges and shows how it
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The source charges are the charges that produce the field. The test charge is a charge used only to probe the field at a location. Because the factor of $q_0$ divides out, the field depends on the source-charge configuration and the location $\vec{r}$, not on the particular test charge used to measure it. By convention, the direction of $\vec{E}$ is the direction of the force on a positive test charge. The SI units of electric field are $\mathrm{N/C}$.}
\wc{Electric field fills all space (even if zero)}{The electric field $\vec{E}$ is defined at every point in space, regardless of whether a test charge is present. At points far from all source charges, the field magnitude may be very small or effectively zero, but the field itself extends throughout space. A test charge placed anywhere will experience $\vec{F}=q\vec{E}$ at that location.}
\thm{Point-charge field law and force relation}{Let a point source charge $Q$ be fixed at position vector $\vec{r}_Q$. Let the field point have position vector $\vec{r}$, and define
\[
\vec{R}=\vec{r}-\vec{r}_Q,