\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}
\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}
\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]
          = 8.99\E{9}\U{N$\cdot$m$^2$/C$^2$} \left(\frac{-6.00\ihat}{0.300^2} - \frac{3.00\jhat}{0.100^2}\right)\E{-9}{C/m^2}
	  = \ans{\left( -0.599\ihat - 2.70\jhat \right)\U{kN/C}}
\end{equation}

\Part{b}
\begin{equation}
 \vect{F} = q_1 \vect{E}
          = \ans{\left( -3.00\ihat -13.5\jhat\right)\U{$\mu$N}}
\end{equation}
\end{solution}
