Dòng chảy năng lượng theo hai dây dẫn điện song song

Hình 1: Điện trường bao quanh hai dây song song

Hình 2: Từ trường bao quanh hai dây song song

Hình 3: Trường vector Poynting – dòng chảy năng lượng dọc theo hai dây dẫn điện song song

Code chương trình Matlab

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function S_field_2_parallel
% Author: Tran Hai Cat
% Lecturer in Physics, HCM University of Technology and Education
% - Dai hoc Su pham Ky thuat Tp. Ho Chi Minh
% Created: 2019.05.03
clc;
clear variables;
close all;

%% CONSTANTS
ke = 9e9;
mu0 = 4*pi*1e-7;

%% PARAMETERS
I = 1; % Ampere
L = 10;
lambda = 2e-9/L;
y_wire_1 = linspace(-2,L,50);
x_wire_1 = -0.5*ones(size(y_wire_1));
z_wire_1 = zeros(size(y_wire_1));

y_wire_2 = linspace(L,-2,50);
x_wire_2 = 0.5*ones(size(y_wire_1));
z_wire_2 = zeros(size(y_wire_1));

Nx = 21;
Ny = 30;
Nz = 21;

xmin = -1.5; xmax = 1.5;
ymin = -1; ymax = L+1;
zmin = -1; zmax = 1;
%% CALCULATION
N = length(x_wire_1)-1;

x = linspace(xmin,xmax,Nx);
y = linspace(ymin,ymax,Ny);
z = linspace(zmin,zmax,Nz);
[X,Y,Z] = meshgrid(x,y,z);

Ex = zeros(size(X));
Ey = zeros(size(Y));
Ez = zeros(size(Z));

Bx = zeros(size(X));
By = zeros(size(Y));
Bz = zeros(size(Z));

kB = mu0/4/pi*I;
cond = [];
for i_wire = 1:N
% wire 1:
dx_wire = x_wire_1(i_wire+1)-x_wire_1(i_wire);
dy_wire = y_wire_1(i_wire+1)-y_wire_1(i_wire);
dz_wire = z_wire_1(i_wire+1)-z_wire_1(i_wire);

Delta_x = X-x_wire_1(i_wire);
Delta_y = Y-y_wire_1(i_wire);
Delta_z = Z-z_wire_1(i_wire);
r = sqrt(Delta_x.^2+Delta_y.^2+Delta_z.^2);

dq = lambda*dy_wire;
E = ke*dq./r./r;
Ex = Ex+E./r.*Delta_x; % x-component of vector field
Ey = Ey+E./r.*Delta_y; % y-component of vector field
Ez = Ez+E./r.*Delta_z; % z-component of vector field

Bx = Bx+kB*(dy_wire*Delta_z-dz_wire*Delta_y)./r.^3; % x-component of vector field
By = By+kB*(dz_wire*Delta_x-dx_wire*Delta_z)./r.^3; % y-component of vector field
Bz = Bz+kB*(dx_wire*Delta_y-dy_wire*Delta_x)./r.^3; % z-component of vector field

cond = [cond;find(r<0.25)];

% wire 2:
dx_wire = x_wire_2(i_wire+1)-x_wire_2(i_wire);
dy_wire = y_wire_2(i_wire+1)-y_wire_2(i_wire);
dz_wire = z_wire_2(i_wire+1)-z_wire_2(i_wire);

Delta_x = X-x_wire_2(i_wire);
Delta_y = Y-y_wire_2(i_wire);
Delta_z = Z-z_wire_2(i_wire);
r = sqrt(Delta_x.^2+Delta_y.^2+Delta_z.^2);

dq = lambda*dy_wire;
E = ke*dq./r./r;
Ex = Ex+E./r.*Delta_x; % x-component of vector field
Ey = Ey+E./r.*Delta_y; % y-component of vector field
Ez = Ez+E./r.*Delta_z; % z-component of vector field

Bx = Bx+kB*(dy_wire*Delta_z-dz_wire*Delta_y)./r.^3; % x-component of vector field
By = By+kB*(dz_wire*Delta_x-dx_wire*Delta_z)./r.^3; % y-component of vector field
Bz = Bz+kB*(dx_wire*Delta_y-dy_wire*Delta_x)./r.^3; % z-component of vector field

cond = [cond;find(r<0.3)];
end
Ex(cond) = 0;
Ey(cond) = 0;
Ez(cond) = 0;
Bx(cond) = 0;
By(cond) = 0;
Bz(cond) = 0;

Sx = (Ey.*Bz-Ez.*By)/mu0; % x-component of vector field
Sy = (Ez.*Bx-Ex.*Bz)/mu0; % y-component of vector field
Sz = (Ex.*By-Ey.*Bx)/mu0; % z-component of vector field

%% DISPLAY RESULTS
figure('name','Electric Field','color','k','numbertitle','off');
hold on
quiver3(X,Y,Z,Ex,Ey,Ez,'AutoScaleFactor',1,'color','r');
axis equal
axis([xmin xmax 0 L zmin zmax]);
rotate3d on
xlabel('X, m');
ylabel('Y, m');
zlabel('Z, m');
view(65,27);
box off
grid off
set(gca,'color','k','xcolor','w','ycolor','w','zcolor','w')
% Draw wires:
plot3(x_wire_1,y_wire_1,z_wire_1,'linewidth',3,'color','cyan');
plot3(x_wire_2,y_wire_2,z_wire_2,'linewidth',3,'color','cyan');

figure('name','Magnetic Field','color','k','numbertitle','off');
hold on
quiver3(X,Y,Z,Bx,By,Bz,'AutoScaleFactor',1,'color','b');
axis equal
axis([xmin xmax 0 L zmin zmax]);
rotate3d on
xlabel('X, m');
ylabel('Y, m');
zlabel('Z, m');
view(65,27);
box off
grid off
set(gca,'color','k','xcolor','w','ycolor','w','zcolor','w')
% Draw wires:
plot3(x_wire_1,y_wire_1,z_wire_1,'linewidth',3,'color','cyan');
plot3(x_wire_2,y_wire_2,z_wire_2,'linewidth',3,'color','cyan');

figure('name','Energy Flux','color','k','numbertitle','off');
hold on
quiver3(X,Y,Z,Sx,Sy,Sz,'AutoScaleFactor',1,'color','g');
axis equal
axis([xmin xmax 0 L zmin zmax]);
rotate3d on
xlabel('X, m');
ylabel('Y, m');
zlabel('Z, m');
view(65,27);
box off
grid off
set(gca,'color','k','xcolor','w','ycolor','w','zcolor','w')
% Draw wires:
plot3(x_wire_1,y_wire_1,z_wire_1,'linewidth',3,'color','cyan');
plot3(x_wire_2,y_wire_2,z_wire_2,'linewidth',3,'color','cyan');