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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