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#+TITLE: Übungsblatt 5 - Aufgabe 3
#+HTML_HEAD_EXTRA: <meta name="robots" content="noindex">
#+SETUPFILE: ../options.org
[[https://thomaslabs.org/shortcoil.m][Quellcode herunterladen]]
* Ergebnisse des Programms
[[https://thomaslabs.org/media/betrag.png]]
[[https://thomaslabs.org/media/richtung.png]]
[[https://thomaslabs.org/media/spulenachse.png]]
* Octave / Matlab Quellcode
#+BEGIN_SRC octave
clear all;
close all;
clc;
%% length of the observed region in m
len = 40e-3; %m
len = len / 2; %we shall go from -len to +len
%% number of points in x- and z-direction
N_space = 50;
%% number of points for integration along coil
N_phi = 250;
%% radius
R = 5e-3; %m
%% length
L = 23e-3; %m
%% number of windings
N = 5;
%% current
I = 8; %A
%% vacuumpermeability
mu0 = 4 * pi * 1e-7; %Vs/Am
%% define grid
z = linspace(-len, len, N_space); %m
x = linspace(-len, len, N_space); %m
%% parameter of coil-wire-path-paramtrisation
phi = linspace(0, N * 2 * pi, N_phi);
dphi = phi(2) - phi(1);
%% Precalculate cos and sin
p_sin = sin(phi);
p_cos = cos(phi);
%% loop through all x-z-points
for iz = 1 : N_space
for ix = 1 : N_space
%% r of this x-z-point
r = [x(ix); 0; z(iz)];
B = [0; 0; 0];
%% Riemann sum along the coil
for ip = 1 : N_phi
%% Point along the coil
l = [R * p_cos(ip); R * p_sin(ip); ip * L / N_phi - L / 2];
%% Vector tangent to the coil of length dl = R * dphi
dl = [- R * p_sin(ip); R * p_cos(ip); L / 2 / N / pi];
dl = (R * dphi / norm(dl)) * dl;
%% Vector from the coil to the x-z-point
rp = r - l;
%% Add dB
B = B + (mu0 / 4 / pi) * I * (1 / norm(rp) ^ 3) * cross(dl, rp);
end
B_X(iz, ix) = B(1);
B_Y(iz, ix) = B(2);
B_Z(iz, ix) = B(3);
end
end
figure('Name', 'Richtung der Flußdichte', 'NumberTitle', 'off');
quiver(x * 1e3, z * 1e3, B_X ./ sqrt(B_X .^ 2 + B_Z .^ 2),
B_Z ./ sqrt(B_X .^ 2 + B_Z .^ 2));
title('Richtung der Flußdichte')
xlabel('x [mm]')
ylabel('z [mm]')
axis image
saveas(gca, 'richtung.png')
betrag = sqrt(B_X .^ 2 + B_Y .^ 2 + B_Z .^ 2)
figure('Name', 'Betrag der Flußdichte', 'NumberTitle', 'off');
imagesc(x * 1e3, z * 1e3, betrag);
title('Betrag der Flußdichte');
xlabel('x [mm]')
ylabel('z [mm]')
colormap(gray);
colorbar('title', 'B [T]');
saveas(gca, 'betrag.png')
figure('Name', 'Flußdichte entlang Spulenachse', 'NumberTitle', 'off');
B_2 = B_Z(:, round((N_space - 1) / 2));
plot(x * 1e3, B_2);
title('Flußdichte entlang Spulenachse');
xlabel('z [mm]');
ylabel('Flußdichte [T]');
saveas(gca, 'spulenachse.png')
#+END_SRC
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