Introductory Programming
Fall 2006


Here's a framework for the particle in a magnetic field problem.

I've put everything in a single file and changed the names of
the functions.

magpart calls ode45, which calls part.

I've removed the bodies of the functions and left the comments

function magpart(te)
% te is the duration of the time range

    % initial conditions
    
    % call ode45
    
    % plot the results
end

function dXdt = part(t, X)
% t is the current time; X contains the position and velocity
% vectors; evaluate the derivative dXdt

end

function A = acceleration(t, P, V)
% t is the current time, P is the position of the particle in
% 3-space, V is the velocity of the particle.  Return the
% total acceleration of the particle.

end

function F = mag_force(t, P, V)
 % t is the current time, P is a position in 3-space
 % V is the current velocity; compute and return the
 % resulting magnetic force

end

function B = mag_field(t, P)
% t is the current time, P is a position in 3-space
% compute and return B, the magnetic field at the given position

end

function F = drag_force(V)
% V is the current velocity; return the resulting drag force

end


If you finish the questions in notes16.txt, try this variation.

The magnetic field around an infinite straight wire is

    mu0 I 
B = -------   L x R
    2 pi r^2

where

mu0 is the constant 4 * pi * 10^-7  (in T m / A)
I is the current in Amps
R is the vector from the nearest point on the wire to P
r is the magnitude of R
L is a unit vector pointing in the direction of current flow


Modify mag_field so it computes B as a function of P for
a wire that runs along the z-axis with 1000 Amps of current
running in the -z direction.

Compute the trajectory of a particle with initial position
P = [-1 0 0] and initial velocity V = [0 0.1 0]

You should include the force of gravity, but no drag.

What happens if you add a very small amount of drag?

What happens if you add more drag?