close all; clear all;

k = 9*10^9;

eps_r = 1;

charge_order = 10^-9;

const = k*charge_order/eps_r;

Nx = 101;

Ny = 101;

n = 2;

E_f = zeros(Nx,Ny);

Ex = E_f;

Ey = E_f;

ex = E_f;

ey = E_f;

r = E_f;

r_square = E_f;

Q = [1,-1];

X = [5,-5];

Y = [0,0];

for k = 1:n

q = Q(k);

for i=1:Nx

for j=1:Ny

r_square(i,j) = (i-51-X(k))^2+(j-51-Y(k))^2;

r(i,j) = sqrt(r_square(i,j));

ex(i,j) = ex(i,j)+(i-51-X(k))./r(i,j);

ey(i,j) = ey(i,j)+(j-51-Y(k))./r(i,j);

end

end

E_f = E_f + q.*const./r_square;

Ex = Ex + E_f.*ex.*const;

Ey = Ex + E_f.*ey.*const;

end

x_range = (1:Nx)-51;

y_range = (1:Ny)-51;

contour_range = -8:0.02:8;

contour(x_range,y_range,E_f',contour_range,'linewidth',0.7);

axis([-15 15 -15 15]);

colorbar('location','eastoutside','fontSize',12);

xlabel('x','fontSize',14);

ylabel('y','fontSize',14);

title('Electric fidld distribution, E (x,y) in V/m','FontSize',14);

V0=0;

m=5;

g=9.81;

rho=1.2;

A=0.09;

cw=0.4;

k=0.5*cw*rho*A;

N=100;

V=zeros(1,N);

V(1)=V0;

deltat=0.2;

for i=1:N-1

V(i+1)=V(i)+deltat*(g-(k/m)*V(i)^2);

end

t=(0:N-1)-deltat;

vterminal=sqrt(g*m/k);

plot(t, V,t,ones(1,N)*vterminal);

xlabel('time in sec'); ylabel('velocity in m/s');

legend ('Euler Method', 'Analytical velocity', 'location', 'south');

npoints = 100;

dt = 1e7;

tau=4.4e9;

N_uranium=zeros(npoints,1);

all zeros

time = zeros(npoints,1);

N_uranium(1) = N_uranium_initial;

N_uranium_initial

time(1) = 0;

for step=1:npoints-1

N_uranium(step+1) = N_uranium(step) - (N_uranium(step)/tau)*dt;

time(step+1) = time(step) + dt;

end

t=0:1e8:10e9;

N_analytical=N_uranium_initial*exp(-t/tau);

plot(time,N_uranium,'r',t,N_analytical,'b');

xlabel('Times in years')

ylabel('Number of atoms')

npoints = 100;

dt = 1e7;

tau=4.4e9;

N_uranium=zeros(npoints,1);

all zeros

time = zeros(npoints,1);

N_uranium(1) = N_uranium_initial;

N_uranium_initial

time(1) = 0;

for step=1:npoints-1

N_uranium(step+1) = N_uranium(step) - (N_uranium(step)/tau)*dt;

time(step+1) = time(step) + dt;

end

t=0:1e8:10e9;

N_analytical=N_uranium_initial*exp(-t/tau);

plot(time,N_uranium,'r',t,N_analytical,'b');

xlabel('Times in years')

ylabel('Number of atoms')

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