1 \begin{problem*}{23.17}
2 A point charge $+2Q$ is at the origin and a point charge $-Q$ is
3 located along the $x$ axis at $x=d$ as in Figure~P23.17. Find a
4 symbolic expression for the net force on a third point charge $+Q$
5 located along the $y$ axis at $y=d$.
13 Charge a = pCharge((0,0), 2, L=Label("$2Q$", align=S));
14 Charge b = nCharge((u,0), -1, L=Label("$-Q$", align=S));
15 Charge c = pCharge((0,u), 1, L=Label("$Q$", align=S));
16 Distance dab = Distance(
17 a.center(), b.center(), offset=0.5u, scale=u, L="$d$");
18 Distance dac = Distance(
19 a.center(), c.center(), offset=-0.5u, scale=u, L="$d$");
21 a.draw(); b.draw(); c.draw(); dab.draw(); dac.draw();
27 Summing the forces from the other two charges
29 \vect{F} = \vect{F}_0 + \vect{F}_x
30 = k\frac{Q\cdot2Q}{d^2}\jhat
31 + k\frac{Q\cdot(-Q)}{d^2+d^2}\frac{-\ihat+\jhat}{\sqrt{2}}
32 = k\frac{Q^2}{d^2}\p({ 2\jhat - \frac{1}{2\sqrt{2}}(-\ihat+\jhat) })
33 = \ans{k\frac{Q^2}{d^2}\p[{ \frac{\ihat}{2\sqrt{2}}
34 + \p({2-\frac{1}{2\sqrt{2}}})\jhat }] }