% lorentz - Program to compute the motion of an electron in% an E and B field using the Euler-Cromer methodclear all; help lorentz; % Clear memory and print header

%@ Initialize variables (e.g., electric and magnetic fields)r = [0 0 0]; % Initial positionv = input('Enter initial velocity [vx vy vz] (m/s) - ');B = [0 0 1]; % B field (points in z-direction);fprintf('Magnetic induction B = [%g %g %g] tesla\n',... B(1),B(2),B(3));E = input('Enter electric field, [Ex Ey Ez] (V/m) - ');dt = 1e-13; % Time step (sec)mass = 9.10939e-31; % Mass of electron (kg)q = 1.602177e-19; % Charge of electron (C)q_over_m = q/mass;

%@ Set up for plotting the electron's motionclf; figure(gcf); % Clear figure window and bring it forwardplot(0,0,'bo'); % Mark the origin with a blue circleXMax = 1.0e-11; XMin = -XMax; % Axis limitsYMin = XMin; YMax = XMax; axis([XMin, XMax, YMin, YMax]);grid on; % Place a hash grid on the graphxlabel('x (m)'); % X-axis labelylabel('y (m)'); % Y-axis labeltitle('Computing motion ...');hold on; % Hold the graph on the screen as points are added

%@ Loop over time steps to compute the motiontime = 0.0;nstep = 1000;for istep=1:nstep

%@ Compute acceleration on electron as a = q/m (E + v X B) v_cross_B = [ (v(2)*B(3)-B(2)*v(3)) ... -(v(1)*B(3)-B(1)*v(3)) ... (v(1)*B(2)-B(1)*v(2)) ]; accel = q_over_m * (E + v_cross_B); %@ Calculate new position and velocity using Euler-Cromer v = v + dt*accel; % Update the velocity r = r + dt*v; % Update the position time = time + dt; % Increment the time %@ Add data point to graph; expand axis limits if needed plot(r(1),r(2),'.','EraseMode','none'); if( r(1) > XMax ) % If position is outside axis limits XMax = 2*XMax; % then increase limits

axis([XMin, XMax, YMin, YMax]); elseif( r(1) < XMin ) % If position is outside axis limits XMin = 2*XMin; % then increase limits

axis([XMin, XMax, YMin, YMax]); elseif( r(2) > YMax ) % If position is outside axis limits YMax = 2*YMax; % then increase limits

axis([XMin, XMax, YMin, YMax]); elseif( r(2) < YMin ) % If position is outside axis limits YMin = 2*YMin; % then increase limits

axis([XMin, XMax, YMin, YMax]); end drawnow; % Redraw the graph

end% Write final title to show that calculation is completetitle(sprintf('Motion of an electron for %g seconds',time));