Code

%% This script draws a plot of the magnetic field for an infinitely long wire

%% Defining constants
one_over_4pic2eps0 = 10^-7;

Current = 100; %Amp


%% defining r and calculating the field strength

r = [0:2000];
B = (2*Current*one_over_4pic2eps0)./r;

%% Plotting field strength;

figure(1);

plot(r,B);
ylim([-1*10^-7, 2*10^-6]);
xlabel('r [m]');
ylabel('|B| [T]');
title('Magnetic field strenght based on distance from infinite wire');

%% Defining vector field r infinite wire
x_values = [-10:0.5:10];
y_values = [-10:0.5:10];

[X_r, Y_r] = meshgrid(x_values, y_values);
X_B = (one_over_4pic2eps0*2*Current).*(-Y_r./(X_r.^2+Y_r.^2));
Y_B = (one_over_4pic2eps0*2*Current).*(X_r./(X_r.^2+Y_r.^2));


%% plotting B field infinite wire

figure(2);
%quiver(X_r, Y_r, X_r, Y_r); %% vector r
quiver(X_r, Y_r, X_B, Y_B); %% vector r
pbaspect([1 1 1]);
xlim([-10 10]);
ylim([-10 10]);

%% calculating for finite wire

X_UnitVecB = -Y_r./sqrt(X_r.^2+Y_r.^2);
Y_UnitVecB =  X_r./sqrt(X_r.^2+Y_r.^2);

%% let the wire start at x=0 and go up to x=length
length = 10;    % meters
x_observer = length/2; % meters
d_cable = 2; % meters

a = [-10:0.001:10]; % meters from wire
theta1 = atan(x_observer./a);
theta2 = atan((length-x_observer)./a);

mu_0 = 4*pi*(10^-7);

mag_B_1 = (mu_0*Current)./((4*pi).*a) .* (sin(theta1) + sin(theta2));
a = a-d_cable;
mag_B_2 = (mu_0*-Current)./((4*pi).*a) .* (sin(theta1) + sin(theta2));

figure(3);
plot(a+(d_cable/2), abs(mag_B_1+mag_B_2));
xlim([-5 5]);
ylim([0 0.001]);
%ylim([-1*10^-9 1*10^-7]);

%% quiver plot
x_values = [-10:0.1:10];
y_values = [-10:0.1:10];

[X1,Y1] = meshgrid(x_values+1, y_values);
wire_1_unit_vecX = -Y1./sqrt(X1.^2+Y1.^2);
wire_1_unit_vecY = X1./sqrt(X1.^2+Y1.^2);

[X2,Y2] = meshgrid(x_values-1, y_values);
wire_2_unit_vecX = Y2./sqrt(X2.^2+Y2.^2);
wire_2_unit_vecY = -X2./sqrt(X2.^2+Y2.^2);

a = sqrt((x_values+1).^2+(y_values).^2);
theta1 = atan(x_observer./a);
theta2 = atan((length-x_observer)./a);
mag_B_1 = (mu_0*Current)./((4*pi).*a) .* (sin(theta1) + sin(theta2));
a = sqrt((x_values-1).^2+(y_values).^2);
theta1 = atan(x_observer./a);
theta2 = atan((length-x_observer)./a);
mag_B_2 = (mu_0*Current)./((4*pi).*a) .* (sin(theta1) + sin(theta2));
unitVecX = wire_1_unit_vecX.*mag_B_1+wire_2_unit_vecX.*mag_B_2;
unitVecY = wire_1_unit_vecY.*mag_B_1+wire_2_unit_vecY.*mag_B_2;
[X, Y] = meshgrid(x_values, y_values);
quiver(X, Y, unitVecX, unitVecY);