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I have a particle moving in a static electromagnetic field in which E and B have the following components:

E=(E_{x}, 0, 0)

B=(-B_{x}, 0, 0)

and both depend on z, namely E_{x}(z) and B_{x}(z).

The particle is moving along z with constant velocity v=(0, 0, v_{z}).

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=v_{z}

dv_{x}/dt= q*E_{x}/m

dv_{y}/dt=q*B_{x}*v_{z}/m

dv_{z}/dt=0

and expressing them as a function of z

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# Lorentz force

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