i received an email about the equations for this simulation.

[color=blue]hi lookang,
this is joshi from India.
A very happy and full of physics new year. Hope you are doing well in life.
I am in a calculation phase of a simulation - 'motion of charge in magnetic field'. so you know that in a complex situation, such as injecting a particle into magnetic field at some angle theta, will make the particle to follow helical trajectory.
since u know that it is better to give liberty to user to orient magnetic field along any direction (i.e. not restricting it along x,y,z - axes). The same is true for velocity also.
Now all references i have referred derive equation of helix considering z-axis as its center axis for sake of simplicity and not any arbitrary axis.
So can u derive/give me a general equation of a helix (with center axis being any 3D line)?
take it as a first challenge (from my side) for our brainstorming friendship.............
chintan joshi[/color]

[b][color=red]my reply is
The equations are as above in the first post
This model is created with the following 6 equations., derivation and checked by lookang
dx/dt = vx
dy/dt = vy
dz/dt = vz
dvx/dt = q*(Ex+(vy*Bz-vz*By))/m
dvy/dt = q*(Ey+(vz*Bx-vx*Bz))/m
dvz/dt = q*(Ez+(vx*By-vy*Bx))/m[/color][/b]