Elektrostatik - Aufgabe 2

Gegebene Größen: Ladungen & Punkt

clear all;
q(1).c = 1; %Coulomb
q(1).pos = [-1 1];
q(2).c = -2;
q(2).pos = [1 0];
q(3).c = 1;
q(3).pos = [-1 -1];
e_0 = 8.854e-12; %C^2/(N m^2)
windowMin = -3;%min([q(:).pos]);
windowMax = 3;%max([q(:).pos]);
% Plot
pos = vertcat(q(:).pos)';
%plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');
%box off;
%grid on;
%hold on;
[X,Y] = meshgrid(linspace(windowMin,windowMax,100)); 
for i = 1:numel(q)
    %Polarkoordinaten (allgemein)
    [q(i).winkel, q(i).rAll] = cart2pol(X-q(i).pos(1),Y - q(i).pos(2));    
end
E_feld = @(q,r) q ./ (4*pi*e_0*r.^2);

Beiträge der E-Felder

%E-Felder Beträge
for i = 1:numel(q)
    q(i).EAll = E_feld(q(i).c,q(i).rAll);
end

Feldvektoren

E_feldvec_x = @(E,winkel) E .* cos(winkel);

E_feldvec_y = @(E,winkel) E .* sin(winkel);

ExAll = zeros(size(X));

EyAll = zeros(size(Y));

%Feldkomponenten

for i = 1:numel(q)

q(i).Ex_All = E_feldvec_x(q(i).EAll,q(i).winkel);

q(i).Ey_All = E_feldvec_y(q(i).EAll,q(i).winkel);

ExAll = ExAll + q(i).Ex_All;

EyAll = EyAll + q(i).Ey_All;

%subplot(1,numel(q),i);

figure,streamslice(X,Y,q(i).Ex_All,q(i).Ey_All); hold on;

plot(q(i).pos(1),q(i).pos(2),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');

box off;

grid on;

xlim([windowMin windowMax]);

ylim([windowMin windowMax]);

%quiver(X,Y,q(i).Ex_All,q(i).Ey_All);

end

Superposition und Endergebnis

EAll = sqrt(ExAll.^2 + EyAll.^2);

%contourf(X,Y,EAll); hold on;

%colormap copper; colorbar;

figure

streamslice(X,Y,ExAll,EyAll); hold on;

plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');

box off;

grid on;

xlim([windowMin windowMax]);

ylim([windowMin windowMax]);