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Homework Help: Particle movement in inhomogeneous magnetic field

  1. Nov 13, 2016 #1
    The problem statement, all variables and given/known data

    Show that for the case of a general inhomogeneous magnetic field, $$\dot{\vec{v}}=\frac{e}{2mc} (\vec{v} \times \vec{B} - \vec{B} \times {v})$$

    The attempt at a solution

    I think I am oversimplifying things. I used that, for an electron in a magnetic field, [itex]m \frac{d \vec{v}}{dt}=e \vec{v} \times \vec{B}[/itex], and that [itex]\vec{v} \times \vec{B} = - \vec{B} \times \vec{v} [/itex]

    Doing this, I find that [itex]RHS = \frac{1}{c} \dot{\vec{v}}[/itex]
     
  2. jcsd
  3. Nov 13, 2016 #2

    TSny

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    The presence of ##c## in the equation is just due to the choice of units.

    May I ask where this problem came from?
     
  4. Nov 13, 2016 #3
    I figured as such, but units for what? B? v? e?

    This problem was not out of a book but was just on a homework sheet, and I was unable to find it elsewhere.
     
  5. Nov 13, 2016 #4

    TSny

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    Compare the Gaussian system of units with the SI units here: https://en.wikipedia.org/wiki/Gaussian_units#Maxwell.27s_equations
    The units for B, v, and e are all different in the two systems: https://en.wikipedia.org/wiki/Gaussian_units#Electromagnetic_unit_names

    OK. It seems odd since, as you say, you can always just rewrite ##\bf{B} \times \bf{v}## as ##-\bf{v} \times \bf{B}## .
     
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