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Homework Help: Modeling an electron in a Magnetic Field

  1. Dec 2, 2006 #1
    I'm not sure where to place this, so please forgive me.

    As you know, an electron experiences a force of F = qVxB in a magnetic field and equating this to centripetral force, we can find the radius of the electron's path to be R = mv/qB Ok, that's simple enough.

    Now, I want to model an electron via 3D graphing in a magnetic field. For this, I need to model every part of its trajectory. This is proving tricky.

    Say we have:

    Bx = 0
    By = 0
    Bz = 1 micro tesla

    The initial electron is coming in at

    Vx = 0
    Vy = 1.5e8 m/s
    Vz = 0

    The cross product is

    Fx = q(VyBz - ByVz)
    Fy = q(VxBz - VzBx)
    Fz = q(VxBy - VyBx)

    Now the acceleration is just a = F / m

    However, For ax I'm getting 4.23e13 m/s^2! which is a wee bit high. Ok, just plain wrong. How would you generate an animation of an electon in a magnetic field? I would like to extend it so the magnetic field osccilates and varies with amplitude versus time.
     
  2. jcsd
  3. Dec 2, 2006 #2
    What is the mass value you used ? Besides, how do you know the value you got is too high ? What exactly did you do.

    Anyhow, the approach and formula's are OK.


    If you wanna incorporate a t-dependent B field, you just need to integrate over time (once and twice) to get velocity and then the trajectory. How does the B field vary (sine, cosine) and along which direction (x,y,z) ? if you know this, just add the components into the right hand side of Fx, Fy and Fz. divide by m to get a and then you start the integrations...

    marlon
     
  4. Dec 2, 2006 #3
    I used the charge of an electron as 1.6022e-19 C and the mass as 9.1e-31 kg which is a charge to mass ratio of 1.76e11!!!!

    My plan was to do it iteratively. To calculate vx, vy, and vz and use rx = rx + vx*dt etc to plot the positions.
     
  5. Dec 2, 2006 #4
    You are forgetting the [tex]t^2[/tex] term. There is a force acting on your system so you also need the [tex]a_x[/tex] part in your equation for [tex]r_x[/tex] !!!


    marlon
     
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