Solve the same boundary value problem as in the previous example but apply the finer mesh shown in the figure below. There are [latex]N_{N} = 21[/latex] nodes and [latex]N_{E} = 24[/latex] triangular elements. In addition, plot the equipotential contours and the electric field between the two surfaces.

1. The potential is found by solving the matrix equation (4.97) using a mesh that is manually generated. The unknown potentials obtained from the MATLAB program are: [latex][V]_{u} = -[S]_{u,u}^{-1}[S]_{u,k}[V]_{k}[/latex] (4.97) [latex]V_{6} = 5.111 V;[/latex] [latex] V_{7} = 5.2222V;[/latex] [latex] V_{8} = 5.7778V;[/latex] [latex] V_{9} = 7.8889V;[/latex] [latex]V_{14} = 5.7778 V;[/latex] [latex]V_{17} = 5.2222 V;[/latex] [latex] V_{20} = 5.1111 V;[/latex] 2. The calculated normalized capacitance for a unit length of the line is C = 10.8444 F. The relative error achieved here is smaller than in the previous example. 3. The equipotential contours are plotted below using the contour function. The electric field is determined using the gradient function and displayed using the quiver function .

Question 4.23: Solve the same boundary value problem as in the previous exa...

Fundamentals of Electromagnetics with MATLAB

Solve the same boundary value problem as in the previous example but apply the finer mesh shown in the figure below. There are $N_{N} = 21$ nodes and $N_{E} = 24$ triangular elements. In addition, plot the equipotential contours and the electric field between the two surfaces.

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1. The potential is found by solving the matrix equation (4.97) using a mesh that is manually generated. The unknown potentials obtained from the MATLAB program are:

$[V]_{u} = -[S]_{u,u}^{-1}[S]_{u,k}[V]_{k}$ (4.97)

$V_{6} = 5.111 V;$ $V_{7} = 5.2222V;$ $V_{8} = 5.7778V;$ $V_{9} = 7.8889V;$

$V_{14} = 5.7778 V;$ $V_{17} = 5.2222 V;$ $V_{20} = 5.1111 V;$

2. The calculated normalized capacitance for a unit length of the line is C = 10.8444 F. The relative error achieved here is smaller than in the previous example.
3. The equipotential contours are plotted below using the contour function. The electric field is determined using the gradient function and displayed using the quiver function .