Question 4.18: Determine the potential distribution within the two adjacent...

Fundamentals of Electromagnetics with MATLAB

Determine the potential distribution within the two adjacent triangular regions if the potential is specified at all nodes

$V_{1} = 8 @ ( 4, 0); V_{2} = 0 @ (0, 0); V_{3} = 0 @ (4, 3);$ and $V_{4} = 8 @ (0, 3).$

4.18

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The voltage distribution in the triangle (1, 2, 3) was determined in Example 4-17 to be $V_{1,2,3}^{(e)} (x,y) = 2x – (8/3 )y$ . The potential distribution within the adjacent triangle (2, 3, 4) is

V_{2,3,4}^{(e)} (x,y) = [1  x  y] \left[\begin{matrix} 1 &0 &0 \\1& 4 & 3 \\ 1& 0 & 3\end{matrix} \right] ^{-1} \left[\begin{matrix}0 \\ 0 \\ 8 \end{matrix} \right]= [1  x  y ]\left[\begin{matrix} 1 & 0 & 0 \\ 0&1/4& -1/4 \\ -1/3& 0 &1/3\end{matrix} \right] \left[\begin{matrix}0 \\ 0 \\ 8 \end{matrix} \right] \\= [1  x  y ] \left[\begin{matrix} 0\\ -2 \\8/3 \end{matrix} \right] = -2x +\frac{8}{3} y

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