Hi,
The code implements Plot of Line Charge distribution on a thin wire which is maintained at V volt.
Here parameters are:
V = 1V
Length of wire, L = 1m
Radius of wire, a = 1mm
The Method of moment technique is used.
The basis function used is Triangular Function,
The testing function used is Delta (Point Matching).
For other specification, Parameters can be changed. For smooth variation the Value of section , N has to be increased.
The outer charge is starting from zero because, the triangular basis function is used from L = 0, The outer most triangular function can be made Half triangular to have high charge density at the ends of the wire.
% Matlab Code for solving Electric potential
% Line charge distribution
% Pulse delta
clc
close all
% clear all;
syms m n
L = 1; % Length of wire
lim1 = 0; % Lower limit
lim2 = L; % Upper limit
a = 0.001; % radius of the wire
V = 1; % Potential V = 1 volt
ep_0 = 8.854*1e-12; % permittivity
ep_r = 1; % relative Permittivity
N = 10; % Number of sections
M = N; % Number of testing function
hx = (lim2-lim1)/(N); % Step width of each section
x = lim1:hx:lim2;
dx = hx;
% Definition of testing function
Zmn = zeros(M,N);
Zmn1 = zeros(M,N);
%Basis function
% 1 for (n-1)delx < x < n*delx
% fn = 1;
ii = 1:N;
xm = (ii-0.5)*dx; % Center for delta function
for n = 1:N
for m = 1:N
xb = n*dx; % Section higher limit
xa = (n-1)*dx; % Section lower limit
if m ==n
Zmn(m,n) = 2*log(dx/a);
else
% p = (xb-xm)+sqrt((xb-xm).^2-a^2); % Caluclation of solution matrix num
% q = (xa-xm)+sqrt((xa-xm).^2-a^2); % Caluclation of solution matrix den
% Zmn(m,n) = log(abs(p/q)); % Getting Zmn matrix
% A(i, j)=DELTA/abs(Y(i)-Y(j) )
Zmn(m,n) = dx/(abs(xm(n)-xm(m)));
end
end
end
% Formation of Zmn matrix
% for m = 1:M
% for n = 1:N
% Zmn1(m,n) = Zmn(m,n);
% end
% end
bm = 4*pi*ep_0*ones(M,1); % Constant Matrix
an = Zmn\bm;
f1 = 0;
fvar = 0;
for n = 1:N
xn = lim1+(n-1)*hx;
if n == 1
fvar = an(n)*rectpuls(x-xn,hx);
else
fvar = an(n)*rectpuls(x-xn,hx);
end
f1 = f1+fvar;
end
figure();
plot(x,f1*1e12,'k--','LineWidth', 2);
title('Plot of charge distribution');
xlabel('section of wire');
ylabel('Charge density (pC/m^3)');
legend(['Computed for N section = ',num2str(N)]);
