Effect of a magnetic field on a bean of particles.

1. Jan 19, 2009

felixthecat

1. The problem statement, all variables and given/known data
a beam of particles of charge q with velocity v is emitted from a point source, roughly parallel with a magnetic field B, but with a small angle of angular dispersion. Show that the effect of the field is to focus the beam to a point at a distance z = 2[/pi]mv/|q|B.

2. Relevant equations
We know the force F= q vxB
dv/dt = -q/m Bxv

3. The attempt at a solution
I try to solve the problem with the force. However, since the beam is roughly parallel to B, the cross product tends to 0. I am now like clueless...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 19, 2009

gabbagabbahey

The initial velocity is approximately parallel to B, not exactly parallel. Try calling the angle between v and B, $\theta$ and calculating r(t) for a particle on the beams outer edge. Then use a Taylor approximation for your expression for small $\theta$ to find the location where r(t) lies on the z-axis (assume that B points in the z-direction).