Commit 54f25c35 authored by Niklas Wahl's avatar Niklas Wahl
Browse files

Alle Skripte hinzugefügt

parent b1d317a7
%% Aufgabe 1
%% Gegeben:
%%
clear all;
d = 1 %m, Ladungsabstand
q_1 = 1 %C
q_2 = -3.5 * q_1
q = [q_1 q_2];
%Bentigt
e_0 = 8.854e-12; %C^2/(N m^2)
%% a)
%%
F = q_1 * q_2 / (4*pi*e_0*d^2)
x = -1.5:0.2:2.5;
y = -2:0.2:2;
[X,Y] = meshgrid(x,y);
q_1_pos = [0 0];
q_2_pos = q_1_pos + [d 0];
[q_1_theta, q_1_rho] = cart2pol(X - q_1_pos(1),Y - q_1_pos(2));
[q_2_theta, q_2_rho] = cart2pol(X - q_2_pos(1),Y - q_2_pos(2));
q_1_pot = q_1 ./ (4*pi*e_0*q_1_rho);
q_2_pot = q_2 ./ (4*pi*e_0*q_2_rho);
E_1 = q_1_pot ./ q_1_rho;
E_2 = q_2_pot ./ q_2_rho;
E_1_x = E_1 .* cos(q_1_theta);
E_2_x = E_2 .* cos(q_2_theta);
E_1_y = E_1 .* sin(q_1_theta);
E_2_y = E_2 .* sin(q_2_theta);
Ex = E_1_x + E_2_x;
Ey = E_1_y + E_2_y;
E_tot = sqrt(Ex.^2 + Ey.^2);
tot_pot = q_1_pot + q_2_pot;
contourf(X,Y, tot_pot);
colormap hot; colorbar; hold on;
streamslice(X,Y,Ex,Ey);
plot([q_1_pos(1),q_2_pos(1)],[q_1_pos(2),q_2_pos(2)],'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b')
%%
\ No newline at end of file
%% Elektrostatik - Aufgabe 2
%% Gegebene Gren: Ladungen & Punkt
clear all;
q(1).c = 25e-9; %Coulomb
q(1).pos = 0.01*[0 4]; %cm
q(2).c = 0.1e-6;
q(2).pos = 0.01*[0 0];
q(3).c = -50e-9;
q(3).pos = 0.01*[-4 3];
e_0 = 8.854e-12; %C^2/(N m^2)
P = 0.01*[0 3];
windowMin = min([q(:).pos P]);
windowMax = max([q(:).pos P]);
% Plot
pos = vertcat(q(:).pos)';
plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');
box off;
grid on;
hold on;
plot(P(1),P(2),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','k');
hold off;
xlim([windowMin windowMax]);
ylim([windowMin windowMax]);
%% Teil a)
%% Krfte
%%
r_12 = norm(q(1).pos - q(2).pos)
F_12 = q(1).c*q(2).c / (4*pi*e_0*r_12^2)
r_23 = norm(q(3).pos - q(2).pos)
F_23 = q(3).c*q(2).c / (4*pi*e_0*r_23^2)
winkel_12 = rad2deg(cart2pol(q(1).pos(1) - q(2).pos(1),q(1).pos(2) - q(2).pos(2)))
winkel_23 = rad2deg(cart2pol(q(3).pos(1) - q(2).pos(1),q(3).pos(2) - q(2).pos(2)))
%Winkel aus aufgabe
alpha_23 = 180 - winkel_23;
alpha_12 = 180 - winkel_12;
%Negativ auf der y-Achse!
F_23_buch = [F_23 * cosd(alpha_23) -F_23 * sind(alpha_23)]
F_12_buch = [F_12 * cosd(alpha_12) -F_12 * sind(alpha_12)]
%Da der koordinatenursprung in der ausgesetzten ladung lag, vorzeichen umdrehen!
F_12 = -1 * [F_12 * cosd(winkel_12) F_12 * sind(winkel_12)]
F_23 = -1 * [F_23 * cosd(winkel_23) F_23 * sind(winkel_23)]
F_res = F_12 + F_23
%%
%% Teil b)
%% Berechne die Abstnde
%%
[X,Y] = meshgrid(linspace(windowMin,windowMax,20));
for i = 1:numel(q)
%Polarkoordinaten (allgemein)
[q(i).winkel, q(i).rAll] = cart2pol(X-q(i).pos(1),Y - q(i).pos(2));
%Aufgabenspezifisch
[q(i).winkel_p, q(i).r_p] = cart2pol(P(1) - q(i).pos(1), P(2) - q(i).pos(2));
q(i).dist = P - q(i).pos;
%q(i).r = norm(q(i).dist);
fprintf('rp_%d = %f\n',i,q(i).r_p);
end
E_feld = @(q,r) q ./ (4*pi*e_0*r.^2);
%% Beitrge der E-Felder
%%
%E-Felder Betrge
for i = 1:numel(q)
q(i).E = E_feld(q(i).c,q(i).r_p);
fprintf('E_%d = %g\n',i, q(i).E);
q(i).EAll = E_feld(q(i).c,q(i).r_p);
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).E_vec(1) = E_feldvec_x(q(i).E,q(i).winkel_p);
q(i).E_vec(2) = E_feldvec_y(q(i).E,q(i).winkel_p);
disp(q(i).E_vec)
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;
%quiver(X,Y,q(i).Ex_All,q(i).Ey_All);
end
%% Superposition und Endergebnis
%%
EP_All = vertcat(q(:).E_vec);
EP_Sup = sum(EP_All,1)
EP = norm(EP_Sup)
EAll = sqrt(ExAll.^2 + EyAll.^2);
contourf(X,Y,EAll); hold on;
colormap copper; colorbar;
quiver(X,Y,ExAll,EyAll);
plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');
box off;
grid on;
hold on;
plot(P(1),P(2),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','k');
xlim([windowMin windowMax]);
ylim([windowMin windowMax]);
\ No newline at end of file
%% Elektrostatik - Aufgabe 3
%% Gegeben:
%%
clear all;
e = 1.609e-19; %C
m_e = 9.11e-31; %kg
d = 0.01; %1cm durchlauf durch plattenkondensator
U_B = 1e3; %1kV
s = 0.002; %0,2 cm Plattenastand
%% Eintrittsgeschwindigkeit
%%
v_0 = sqrt(2*e*U_B / m_e)
%% Zeit
%%
t = d / v_0
%% Ablenkung
%%
U = m_e * s^2 * v_0^2 / e / d^2
\ No newline at end of file
%% Elektrostatik - Aufgabe 4
%% Gegeben:
%%
clear all;
d = 5; %m
E = 1000; %V/m
%% Flche
%%
A = (d/2)^2 * pi
%% Fluss
%%
Phi_el = E*A
%%
\ No newline at end of file
%% Elektrostatik - Aufgabe 5
%% Gegeben:
%%
clear all;
r1 = 1e-3; %1mm
r2 = 1; %1m
q1 = 5e-12; %5 pC
q2 = 0.02e-9; %0.02 nC
r3 = 0.1;
%Zustzliche Kosntanten
e_0 = 8.854e-12; %C^2 / (N m^2)
%% Potentiale
%%
phi = @(q,r) q ./ (4*pi*e_0*r);
phi1 = phi(q1,r1)
phi2 = phi(q1,r2)
%% Spannung
%%
U = phi1 - phi2
%% Energie
%%
W1 = q1 * U
%% Arbeit an Probeladung q2
%%
W2 = q2 * phi(q1,r3)
\ No newline at end of file
%% Elektrostatik - Aufgabe 6
%% Gegebene Gren: Ladungen & Punkt
clear all;
q(1).c = 10e-9; %Coulomb
q(1).pos = 0.001*[0 2]; %cm
q(2).c = -4e-9; %C
q(2).pos = 0.001*[2 0];
q(3).c = -2.5e-9;
q(3).pos = 0.001*[4 2];
e_0 = 8.854e-12; %C^2/(N m^2)
P = 0.001*[2 4];
windowMin = min([q(:).pos P]);
windowMax = max([q(:).pos P]);
% Plot
pos = vertcat(q(:).pos)';
plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');
box off;
grid on;
hold on;
plot(P(1),P(2),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','k');
hold off;
%% Potentiale
%%
[X,Y] = meshgrid(linspace(windowMin,windowMax,20));
phi = @(q,r) q ./ (4*pi*e_0*r);
phiAll = zeros(size(X));
for i = 1:numel(q)
%Polarkoordinaten (allgemein)
[q(i).winkel, q(i).rAll] = cart2pol(X-q(i).pos(1),Y - q(i).pos(2));
q(i).phiAll = phi(q(i).c,q(i).rAll);
phiAll = phiAll + q(i).phiAll;
%Aufgabenspezifisch
q(i).dist = P - q(i).pos;
q(i).r = norm(q(i).dist);
fprintf('rp_%d = %f\n',i,q(i).r);
q(i).phi = phi(q(i).c,q(i).r);
fprintf('phi_%d = %f\n',i,q(i).phi);
end
%% Superposition und Endergebnis
%%
phi_P = sum([q(:).phi])
contourf(X,Y,phiAll); hold on;
colormap copper; colorbar;
plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');
box off;
grid on;
hold on;
plot(P(1),P(2),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','k');
\ No newline at end of file
%% Elektrostatik - Aufgabe 7
%% Gegeben:
%%
clear all;
s = 0.05;
d = 0.001;
U = 12;
e_r = 2;
%Zustzliche Kosntanten
e_0 = 8.854e-12; %C^2 / (N m^2)
%% Teil a)
%% Kapazitt
%%
C = @(e_r,A,d) e_0*e_r*A/d;
C_a = C(e_r,s^2,d)
%% Ladung
%%
Q = C_a * U
%% Teil b)
%% Kapazitten
%%
C_1 = C(e_r, s^2, d/2)
C_2 = C(1,s^2,d/2)
%% Gesamtkapazitte (Reihenschaltung)
C_ers = C_1*C_2 / (C_1 + C_2)
%% Ladung
%%
Q = C_ers * U
\ No newline at end of file
%% Elektrostatik - Aufgabe 8
%% Gegeben:
%%
clear all;
U = 8
C1 = 5e-12
C2 = 3 * C1
C3 = 0.01e-9
C5 = 1e-12
C4 = 0.5*C5
C6 = 0.5*C1
%% Kapazitten
%%
C_Reihe = @(Cs) 1 / sum(1./Cs);
C_Parallel = @(Cs) sum(Cs);
Cers12 = C_Reihe([C1,C2])
Cers123 = C_Parallel([Cers12,C3])
Cers456 = C_Reihe([C4 C5 C6])
Cges = C_Reihe([Cers123 Cers456])
%% Ladungen
%%
Qges = Cges * U
U4 = Qges / C4
U5 = Qges / C5
U6 = Qges / C6
U3 = Qges / Cers123
Q3 = U3 * C3
Q1 = U3*Cers12
Q2 = Q1
\ No newline at end of file
%% Wie rechne ich.. die berlagerung elektrischer Felder aus?
%% Ladungen & Punkt
%%
clear all;
q(1).c = 1; %Coulomb
q(1).pos = [0 0]; %cm
q(2).c = 3;
q(2).pos = [4 2];
q(3).c = -2;
q(3).pos = [3 4];
P = [0 4];
% Plot
windowMin = min([q(:).pos P]) - 1;
windowMax = max([q(:).pos P]) + 1;
pos = vertcat(q(:).pos)';
plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');
box off;
grid on;
hold on;
plot(P(1),P(2),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','k');
xlim([windowMin windowMax]);
ylim([windowMin windowMax]);
%% Berechne die Abstnde
%%
[X,Y] = meshgrid(linspace(windowMin,windowMax,100));
%Abstnde
for i = 1:numel(q)
q(i).dist = P - q(i).pos;
q(i).r = norm(q(i).dist);
fprintf('r_%d = %f\n',i,q(i).r);
q(i).rAll = arrayfun(@(x,y) norm([x y] - q(i).pos),X,Y);
end
e_0 = 8.854e-12; %C^2/(N m^2)
E_feld = @(q,r) q ./ (4*pi*e_0*r.^2);
%% Beitrge der E-Felder
%%
%E-Felder Betrge
for i = 1:numel(q)
q(i).E = E_feld(q(i).c,q(i).r * 0.01); %r in m!
fprintf('E_%d = %g\n',i, q(i).E);
q(i).EAll = E_feld(q(i).c,q(i).r * 0.01);
end
%% Berechnung der Winkel (-> Polarkoordinaten)
%%
%Winkel
for i = 1:numel(q)
q(i).winkel = arrayfun(@(x,y) cart2pol(x-q(i).pos(1),y - q(i).pos(2)),X,Y);
%p_cos = [P(1) - q(i).pos(1)] / q(i).r;
p_sin = [P(2) - q(i).pos(2)] / q(i).r;
q(i).p_alpha = asind(p_sin);
q(i).p_polar = cart2pol(P(1)-q(i).pos(1),P(2) - q(i).pos(2));
fprintf('alpha_%d = %f\n',i,q(i).p_alpha);
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).E_vec(1) = E_feldvec_x(q(i).E,q(i).p_polar);
q(i).E_vec(2) = E_feldvec_y(q(i).E,q(i).p_polar);
disp(q(i).E_vec)
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;
%quiver(X,Y,q(i).Ex_All,q(i).Ey_All);
end
%% Superposition und Endergebnis
%%
EP_All = vertcat(q(:).E_vec);
EP_Sup = sum(EP_All,1);
disp(EP_Sup);
EP = norm(EP_Sup);
disp(EP);
EAll = sqrt(ExAll.^2 + EyAll.^2);
contourf(X,Y,EAll);
colormap pink; colorbar;
%quiver(X,Y,ExAll,EyAll);
hold off;
streamslice(X,Y,ExAll,EyAll); hold on;
plot(pos(1,:),pos(2,:),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','b');
box off;
grid on;
plot(P(1),P(2),'LineStyle','None','Marker','o','MarkerSize',10,'MarkerFaceColor','k');
xlim([windowMin windowMax]);
ylim([windowMin windowMax]);
\ No newline at end of file
%% Wie rechne ich.. Elektronenvolt in Joule um?
%% Gegeben:
%%
clear all;
eV = 3
J = 5.8e-10
e = 1.609e-19; %C
%% Ergebnis
%%
eV2J = 3 * e
J2eV = J / e
\ No newline at end of file
%% Wie rechne ich.. die Elektronenablenkung in einer Braun'schen Rhre?
%% Gegeben:
%%
clear all;
x = 0.01; %1cm
v_x = 9e6; %m/s
E_y = 1000; %N/C;
q = 1.609e-19; %C
m_e = 9.11e-31; %kg
g = 9.81; %m/s
d = 0.2; %20cm
%% Zeit
%%
t = x ./ v_x
%% Spielt die Gravitationskraft eine Rolle?
%%
F_el = q * E_y;
F_G = m_e * g;
verhaeltnis = F_el / F_G
%% Ablenkung
%%
%F == F_el
a = q*E_y / m_e
y_1 = 0.5*a*t^2
v_y = a * t
alpha = atand(v_y / v_x)