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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