Motion in B Field: Solve for Focussing Distance

[bon]

Homework Statement

Particles with charge e and mass m are emitted with velocity v from a point source. Their directions of emission make a small angle with the direction of a uniform constant flux density B. Show that the particles are focussed to a point at a distance 2pi mv/Be from their source and at integral multiples of this distance.

Homework Equations

The Attempt at a Solution

Not sure how to do this.?

Obviously we need to use the Loretnz force: F = q(v x B) but can't seem to get the result...

Help please ! :)

 

[cragar]

well if you set the Lorentz force equal to the centripetal force and solve for r
you get $$r= \frac{mv}{eB}$$

 

[bon]

Sorry but that doesn't really help at all. Anyone else?

 

[Zacku]

Hi,

I don't know if it's the most clever thing to do but at least you can try to solve the whole trajectory for one electron. I don't know if you already know how to do it but if not, can you write down Newton's second law of dynamics for the Lorentz force?

That would be definitely a starting point .

 

[bon]

Yep, have already solved that EOM thanks. Still stuck though...

 

[Zacku]

So you have already, say, x(t), y(t) and z(t) as a function of the initial conditions and e,m and B?