Lorentz force

1. Feb 3, 2012

1Keenan

Hi,

I have a particle moving in a static electromagnetic field in which E and B have the following components:
E=(Ex, 0, 0)
B=(-Bx, 0, 0)
and both depend on z, namely Ex(z) and Bx(z).
The particle is moving along z with constant velocity v=(0, 0, vz).

If I want to express Lorentz force as a function of z, is it correct to write:

F(z)=q [(E *cross (1/v)) *cross (1/v) + B *cross (1/v)]?

I get this equation considering F=q(E+v *cross B) as a system of 6 differential equations:

dx/dt=0
dy/dt=0
dz/dt=vz
dvx/dt= q*Ex/m
dvy/dt=q*Bx*vz/m
dvz/dt=0

and expressing them as a function of z

2. Feb 3, 2012

tiny-tim

Hi 1Keenan!
No.
(write "x" not "*cross" )

Where do the 1/v come from?

3. Feb 3, 2012

1Keenan

Why?
My particle is moving along z and v=[0,0,vz]
of course it will have a displacement along x and y but the intial velocity has only one component.

it comes from the differential equation:
dvx/dt=qEx/m
dvy/dt=qBxvz/m

I change the variable t in z... it is a bit of algebra I can write you everything if you want so you can double check my manipulation.

4. Feb 3, 2012

tiny-tim

but that doesn't mean that dx/dt = dy/dt = 0, not even initially
i still don't get it

5. Feb 3, 2012

1Keenan

What does it mean?

How do you write it down?
I don't understand what is tricky for you....

6. Feb 3, 2012

1Keenan

I was thinking, and actually I'm doing something stupid, but I'm really interested in expressing those differential equation as function of z and I'm lost in papers full of my wrong formulas...
at the moment I'm not able to calculate 1+1.... :(