\begin{problem*}{23.17}
A point charge $+2Q$ is at the origin and a point charge $-Q$ is
located along the $x$ axis at $x=d$ as in Figure~P23.17.  Find a
symbolic expression for the net force on a third point charge $+Q$
located along the $y$ axis at $y=d$.
\begin{center}
\begin{asy}
import Mechanics;
import ElectroMag;

real u = 1.5cm;

Charge a = pCharge((0,0), 2, L=Label("$2Q$", align=S));
Charge b = nCharge((u,0), -1, L=Label("$-Q$", align=S));
Charge c = pCharge((0,u), 1, L=Label("$Q$", align=S));
Distance dab = Distance(
    a.center(), b.center(), offset=0.5u, scale=u, L="$d$");
Distance dac = Distance(
    a.center(), c.center(), offset=-0.5u, scale=u, L="$d$");
draw_ijhat((0,0));
a.draw(); b.draw(); c.draw(); dab.draw(); dac.draw();
\end{asy}
\end{center}
\end{problem*}

\begin{solution}
Summing the forces from the other two charges
\begin{equation}
  \vect{F} = \vect{F}_0 + \vect{F}_x
    = k\frac{Q\cdot2Q}{d^2}\jhat
      + k\frac{Q\cdot(-Q)}{d^2+d^2}\frac{-\ihat+\jhat}{\sqrt{2}}
    = k\frac{Q^2}{d^2}\p({ 2\jhat - \frac{1}{2\sqrt{2}}(-\ihat+\jhat) })
    = \ans{k\frac{Q^2}{d^2}\p[{ \frac{\ihat}{2\sqrt{2}}
                               + \p({2-\frac{1}{2\sqrt{2}}})\jhat }] }
\end{equation}
\end{solution}
