1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

    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}## .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Particle movement in inhomogeneous magnetic field
Loading...