User:Foxjwill/Sandbox

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[rtsp://real.cbsig.net/cbsnews/archive/2006/11/22/video2205030.rm]

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[edit] Gnuplot vector field thingy

[edit] 1

r(x,y) = \sqrt{x^2 + y^2}


\begin{align} F_1 (x,y) &= \frac{q_1}{r(x-x_0,y)}\\ F_2 (x,y) &= \frac{q_2}{r(x+x_0,y)}\\ \end{align}

[edit] 2

\sum F = F_1(x,y) + F_2(x,y)

[edit] 3

\begin{align} e_{1x} (x,y) &= \frac{q_1 \cdot (x-x_0)}{r(x-x_0,y)^3}\\ e_{1y} (x,y) &= \frac{q_1 \cdot y}{r(x-x_0,y)^3}\\ \\ e_{2x} (x,y) &= \frac{q_2 \cdot (x+x_0)}{r(x+x_0,y)^3}\\ e_{2y} (x,y) &= \frac{q_2 \cdot y}{r(x+x_0,y)^3}\\ \\ \sum e_x (x,y) &= e_{1x}(x,y) + e_{2x}(x,y)\\ \sum e_y (x,y) &= e_{1y}(x,y) + e_{2y}(x,y)\\ \end{align}


\begin{align} |e (x,y)| &= \sqrt{ \left( \sum e_x (x,y)\right )^2 + \left( \sum e_y (x,y)\right )^2}\\ \\ d_{x1} (x,y) &= \frac{coef \sum e_x (x,y)}{|e (x,y)|}\\ d_{y1} (x,y) &= \frac{coef \sum e_y (x,y)}{|e (x,y)|}\\ \\ d_{x2} (x,y) &= coef \sum e_x (x,y)\\ d_{y2} (x,y) &= coef \sum e_y (x,y)\\ \end{align}