4k_eqa/x^3$.
\end{problem*} % problem 19.16
-\empaddtoprelude{
- pair A, B;
- numeric a;
- a := 1cm;
- A := (-a,0);
- B := (a, 0);
- C := (6a, 0);
- def drawC =
- drawarrow (A-(a,0))--(C+(a,0)) withpen pencircle scaled 0pt;
- draw_ncharge(A, 6pt);
- draw_pcharge(B, 6pt);
- label.top("0", draw_ltic(origin, 90, 0, 3pt, 0pt, black));
- dotlabel.bot("x", C);
- label.bot("a", draw_length(A, origin, 10pt));
- label.bot("a", draw_length(origin, B, 10pt));
- labeloffset := 8pt;
- label.top("-q", A);
- label.top("q", B);
- enddef;
-}
-
\begin{nosolution}
\begin{center}
-\begin{empfile}[3p]
-\begin{emp}(0cm, 0cm)
- drawC;
-\end{emp}
-\end{empfile}
+\begin{asy}
+import ElectroMag;
+
+real u = 0.5cm;
+Vector ihat = ihat();
+ihat.mag = 4u;
+ihat.label = Label("$x$", position=EndPoint, align=RightSide);
+ihat.draw();
+Charge a = nCharge((-u, 0), Label("$-q$", align=S)); a.draw();
+Charge b = pCharge((u, 0), Label("$+q$", align=S)); b.draw();
+Distance da = Distance(a.center(), (0,0), "$a$", offset=-12pt); da.draw();
+Distance db = Distance((0,0), b.center(), "$a$", offset=-12pt); db.draw();
+\end{asy}
\end{center}
\end{nosolution}
\begin{solution}
\begin{center}
-\begin{empfile}[3]
-\begin{emp}(0cm, 0cm)
- label.top(btex $E_{q}$ etex, draw_Efield(B, C, 18pt));
- label.top(btex $E_{-q}$ etex, draw_Efield(A, C, -16pt));
- drawC;
-\end{emp}
-\end{empfile}
+\begin{asy}
+import ElectroMag;
+
+real u = 0.5cm;
+Vector ihat = ihat();
+ihat.mag = 9u;
+ihat.label = Label("$x$", position=EndPoint, align=RightSide);
+ihat.draw();
+Charge a = nCharge((-u, 0), Label("$-q$", align=S)); a.draw();
+Charge b = pCharge((u, 0), Label("$+q$", align=S)); b.draw();
+Distance da = Distance(a.center(), (0,0), "$a$", offset=-12pt); da.draw();
+Distance db = Distance((0,0), b.center(), "$a$", offset=-12pt); db.draw();
+Charge cs[] = {a, b};
+string subscripts[] = {"-", "+"};
+pair c = (6u, 0);
+CoulombEFields(c, cs, subscripts, scale=c.x, unit=u);
+dot(c);
+\end{asy}
\end{center}
Let us assume the point in question has a positive $x$ value (just
reverse the sign if $x < 0$).