\Part{b} What is the resultant force on $q_4$?
\end{problem*} % problem 19.15
-\empaddtoprelude{
- numeric a;
- pair A, B, C, D;
- a := 1cm;
- A := (0, a); % q1, labeled CCW from upper left
- B := origin; % q2
- C := (a, 0); % q3
- D := (a, a); % q4
- def drawE =
- label.lft("a", draw_length(A, B, 8pt));
- label.bot("a", draw_length(B, C, 8pt));
- labeloffset := 5pt;
- draw_pcharge(A, 3pt);
- label.bot(btex $q_1$ etex, A);
- draw_pcharge(B, 3pt);
- label.top(btex $q_2$ etex, B);
- draw_pcharge(C, 3pt);
- label.top(btex $q_3$ etex, C);
- draw_pcharge(D, 3pt);
- label.bot(btex $q_4$ etex, D);
- enddef;
-}
\begin{nosolution}
\begin{center}
-\begin{empfile}[5ns]
-\begin{emp}(0cm,0cm)
- drawE;
-\end{emp}
-\end{empfile}
+\begin{asy}
+import ElectroMag;
+
+real u = 2cm;
+draw(scale(u)*unitsquare, dashed);
+Charge a = aCharge((0, u), q=2, Label("$q_1$", align=W)); a.draw();
+Charge b = aCharge((0, 0), q=3, Label("$q_2$", align=W)); b.draw();
+Charge c = aCharge((u, 0), q=4, Label("$q_3$", align=E)); c.draw();
+Charge d = aCharge((u, u), q=4, Label("$q_4$", align=E)); d.draw();
+label("$a$", (u/2, 0), align=S);
+\end{asy}
\end{center}
\end{nosolution}
\begin{solution}
\begin{center}
-\begin{empfile}[5]
-\begin{emp}(0cm,0cm)
- label.rt(btex $E_{14}$ etex, draw_Efield(A, D, 0.5cm));
- label.urt(btex $E_{24}$ etex, draw_Efield(B, D, 0.53cm));
- label.lft(btex $E_{34}$ etex, draw_Efield(C, D, 1cm));
- draw_ijhats((-1.5*a, a/3), 0, a/3);
- drawE;
-\end{emp}
-\end{empfile}
+\begin{asy}
+import ElectroMag;
+
+real u = 2cm;
+draw(scale(u)*unitsquare, dashed);
+Charge a = aCharge((0, u), q=2, Label("$q_1$", align=W)); a.draw();
+Charge b = aCharge((0, 0), q=3, Label("$q_2$", align=W)); b.draw();
+Charge c = aCharge((u, 0), q=4, Label("$q_3$", align=E)); c.draw();
+Charge d = aCharge((u, u), q=1, Label("$q_4$", align=SE)); d.draw();
+label("$a$", (u/2, 0), align=S);
+Charge cs[] = {a, b, c};
+CoulombEFields(d.center(), cs, scale=u, unit=u/4);
+Vector F = CoulombForce(a, d, scale=u, unit=u/4)
+ + CoulombForce(b, d, scale=u, unit=u/4)
+ + CoulombForce(c, d, scale=u, unit=u/4);
+F.label = Label("$F$", position=EndPoint, align=RightSide);
+F.draw();
+\end{asy}
\end{center}
Let \ihat\ point to the right and \jhat\ point up.
\begin{equation}