Motion of a charged particle in a static magnetic field in matlab

[gursimran]

I want to simulate this type of situation but for simplicity I'm implementing it in 2d at first.. by setting the initial velocity 0 in parallel to B.

Homework Statement

mass of particle is given assume anything
charge
magnitude of B
initial velocity

Homework Equations

The Attempt at a Solution

% script that simulates a moving particle with some initial velocity in a
% magnetic field B

v0 = [5 0 0]; %initial velocity
B = [0 0 -5]; %magnitude of B
m = 5; % mass
q = 1; % charge on particle
r0 = [0 0 0]; % initial position of particle
t = 0;

% Now we want to find the next velocity as the particle enters the magnetic
% field and hence its new position

r = r0;
v = v0;
dt = 0.00000000000000000001;

figure
xlim([-25 25])
ylim([-25 25])
hold on

for n = 1:100
%plot it
plot(r(1),r(2),'*');
%pause

% update time
t = t+dt;

% new position r
dr = v*dt;
r = r + dr;

%find new velocity
dv = (q/m) * cross(v,B);
v = v + dv;


end


I know the most probable reason is the quantissation error but I'm not able to figure out that how can I avoid this error and simulate the situation in MATLAB ..

 

[nilesh_pat]

The quantization error can be avoided by using a larger time step for the simulation. You could also use a numerical integration technique that is more accurate, such as Runge-Kutta or Euler's method. Additionally, you could consider increasing the number of iterations of the loop in order to improve the accuracy of the simulation.