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Lorentz force

  1. Feb 3, 2012 #1
    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. jcsd
  3. Feb 3, 2012 #2

    tiny-tim

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    Hi 1Keenan! :smile:
    No. :confused:
    (write "x" not "*cross" :wink:)

    Where do the 1/v come from? :confused:
     
  4. Feb 3, 2012 #3
    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.
    Could you please explain your point?



    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.
     
  5. Feb 3, 2012 #4

    tiny-tim

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    but that doesn't mean that dx/dt = dy/dt = 0, not even initially :redface:
    i still don't get it :redface:
     
  6. Feb 3, 2012 #5
    What does it mean? :confused:

    How do you write it down?
    I don't understand what is tricky for you....
     
  7. Feb 3, 2012 #6
    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.... :(
     
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