[quote author=Fu-Kwun Hwang link=topic=33.msg7530#msg7530 date=1290056595]
Just apply the Lorentz's force \vec{F}=q\vec{v}\times\vec{B} to your simulation.
For B field in z direction, velocity in x-y plane.
F_x=q*v_y*B_z
F_y=-q*v_x*B_z
or the differential equations are
\frac{d^2v_x}{dt}=\frac{q}{m}v_y*Bz
\frac{d^2v_y}{dt}=-\frac{q}{m}v_x*Bz

And you can check out whether v=\sqrt{v_x*v_x+v_y*v_y} is a constant or not.
[/quote]

thx a lot..
but  actually I  don't understand so much , you write (Fx with Vy) and (Fy with Vx) I don't know why??

I see that you have studied the physics by dropping the vectors in the axises but I studied it by vectors
i.e :
in the gap vectors will be like this in first picture , then I conclude the next velocity vector V2 ( I mean velocity vector in the next moment , I have divided the time into amounts and study the motion of the charged particle in every moment ) by adding the tow V1 and acc ,according to the equation of the direct motion ,since if we study the motion in a very little  moment the motion will be straight , then the new velocity vector will increase and this is really because we know that velocity is increase in the gap ...

but in the dee velocity must be constant as we know , but please look at the second picture ,where I conclude V2 by adding  V1 and acc vectors
it will not be constant never but we know that in the dee velocity vector is constant  ..this is my problem  :(

I hope you understand me  :-[