\begin{problem*}{19.13}
Three point charges are arranged as shown in Figure P19.13.\\
-%\begin{center}
-% \begin{tabular}{|l|r|r|r|}
-% Name & Charge (nC) & x (m) & y (m) \\
-% \hline
-% $q_1$ & $5.00$ & $0$ & $0$ \\
-% $q_2$ & $6.00$ & $0.300$ & $0$ \\
-% $q_3$ & $-3.00$ & $0$ & $-0.100$ \\
-% \hline
-% \end{tabular}
-%\end{center}
\Part{a} Find the vector electric field \vect{E} that $q_2$ and $q_3$
together create at the origin.
\Part{b} Find the vector force \vect{F} on $q_1$.
\end{problem*} % problem 19.13
-\empaddtoprelude{
- numeric a;
- pair A, B, C;
- a := 3cm;
- A := origin; % q1
- B := (a,0); % q2
- C := (0,-a/3); % q3
- def drawB =
- label.top(btex 0.300\mbox{ m} etex, draw_length(B, A, 8pt));
- label.lft(btex 0.100\mbox{ m} etex, draw_length(A, C, 8pt));
- labeloffset := 6pt;
- draw_pcharge(A, 4pt);
- label.rt(btex $q_1 = 5\mbox{ nC}$ etex, A);
- draw_pcharge(B, 4.2pt);
- label.rt(btex $q_2 = 6\mbox{ nC}$ etex, B);
- draw_ncharge(C, 3pt);
- label.rt(btex $q_3 = -3\mbox{ nC}$ etex, C);
- enddef;
-}
-
\begin{nosolution}
\begin{center}
-\begin{empfile}[2p]
-\begin{emp}(0cm,0cm)
- drawB;
-\end{emp}
-\end{empfile}
+\begin{asy}
+import ElectroMag;
+
+real u = 20cm;
+draw_ijhat();
+Charge a = aCharge((0, 0), q=5, Label("$q_1=5.00\U{nC}$", align=W));
+a.draw();
+Charge b = aCharge((0.3u, 0), q=6, Label("$q_2=6.00\U{nC}$", align=S));
+b.draw();
+Charge c = aCharge((0, -0.1u), q=-3, Label("$q_3=-3.00\U{nC}$", align=S));
+c.draw();
+Distance dab = Distance(a.center(), b.center(), offset=-24pt, L="$0.300\U{m}$");
+dab.draw();
+Distance dac = Distance(a.center(), c.center(), L="$0.100\U{m}$");
+dac.draw();
+\end{asy}
\end{center}
\end{nosolution}
\begin{solution}
\begin{center}
-\begin{empfile}[2]
-\begin{emp}(0cm,0cm)
- label.lft(btex $E_{21}$ etex, draw_Efield(B, A, a/8));
- label.rt(btex $E_{31}$ etex, draw_Efield(C, A, -a/5));
- draw_ijhats(-(a, a/3), 0, a/6);
- drawB;
-\end{emp}
-\end{empfile}
+\begin{asy}
+import ElectroMag;
+
+real u = 20cm;
+draw_ijhat();
+Charge a = aCharge((0, 0), q=5, Label("$q_1=5.00\U{nC}$", align=dir(160)));
+a.draw();
+Charge b = aCharge((0.3u, 0), q=6, Label("$q_2=6.00\U{nC}$", align=S));
+b.draw();
+Charge c = aCharge((0, -0.1u), q=-3, Label("$q_3=-3.00\U{nC}$", align=S));
+c.draw();
+Distance dab = Distance(a.center(), b.center(), offset=-24pt, L="$0.300\U{m}$");
+dab.draw();
+Distance dac = Distance(a.center(), c.center(), offset=-24pt,
+ L=Label("$0.100\U{m}$", align=LeftSide));
+dac.draw();
+Charge cs[] = {b, c};
+string subscripts[] = {"2", "3"};
+CoulombEFields(a.center(), cs, subscripts, scale=0.1u, unit=0.03u);
+Vector F = CoulombForce(b, a, scale=0.1u, unit=0.006u)
+ + CoulombForce(c, a, scale=0.1u, unit=0.006u);
+F.label = Label("$F$", position=EndPoint, align=RightSide);
+F.draw();
+\end{asy}
\end{center}
\Part{a}
-\begin{equation}
\begin{equation}
\vect{E} = k_e \sum_i \frac{q_i}{r_i^2}\rhat_i
= k_e \left[\frac{q_2}{x_2^2}(-\ihat) + \frac{q_3}{y_3^2}\jhat\right]