Question 3.16: Write a MATLAB program to: 1) Calculate the potentials in t...
Write a MATLAB program to:
1) Calculate the potentials in the three free nodes with # = 4, 5, 9;
2) Calculate the total electrostatic energy W stored between the plates and find the capacitance C0 of 1m of the line.
Use a simple regular mesh shown in the figure and the following numerical values for the parameters: a = 1 cm, b = 2 cm, V = 10 V on the outer conductor, and V = 0 V on the inner conductor. In this case, there are NN = 11 nodes and NE = 12 elements.
1) The potential is found by solving the matrix equation (3.78) using there a mesh that is manually generated.
[ V ]_{ u }=-[ S ]_{ u , u }{ }^{-1}[ S ]_{ u , k }[ V ]_{ k } \equiv[ F ][ V ]_{ k } (3.78)
The unknown potentials calculated with the MATLAB program are:
V4 = 5V ; V5 = 7.5 V ; V9 = 5 V .
2) The calculated normalized capacitance (C = C0 / ε0 ) per unit length of the line calculated from (3.79) is C = 11.0.
C_{0}=\frac{2 W}{V^{2}} (3.79)
The value, found in the literature for this square coaxial line with b = 2a , is C = 10.2341. The accuracy can be improved by increasing the number of the nodes and elements which will be shown in the next example.