1. Not finding help here? Sign up for a free 30min 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!

Lorentz force and Newton's law

  1. Oct 24, 2011 #1
    1. The problem statement, all variables and given/known data

    This problem asks you to work out the dielectric function of a gas of particles with number density n, charge q, and mass m, with a steady magnetic field applied in the z direction.

    Assume an electric field in the x direction,

    [tex] E_x(t)=E_xe^{-i \omega t} [/tex]

    is applied. Write down the x and y components of the Newton’s Law using the Lorentz force equation and no damping. Assume a solution for the velocity of the form,

    [tex] v_x(t)=v_{x0}e^{-i \omega t} [/tex]

    and

    [tex] v_y(t)=v_{y0}e^{-i \omega t} [/tex]

    Solve for v_x0 and v_y0 in terms of E_x and the cyclotron frequency,

    [tex] \omega_c = qB/m [/tex]

    2. Relevant equations

    [tex] \mathbf{F}=q(\mathbf{E}+\mathbf{v}\times \mathbf{B}) [/tex]

    [tex] \mathbf{F}=m \mathbf{a} [/tex]


    3. The attempt at a solution

    [tex] m \frac{d \mathbf{v}}{dt}=q(\mathbf{E}+\mathbf{v}\times \mathbf{B}) [/tex]

    [tex] \frac{dv_x}{dt}=-i \omega v_{x0}e^{-i \omega t} [/tex]

    [tex] \frac{dv_y}{dt}=-i \omega v_{y0}e^{-i \omega t} [/tex]

    I am having trouble pulling all these equations to write out the components of Newton's law.
     
    Last edited: Oct 24, 2011
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Lorentz force and Newton's law
  1. Newton's laws- pulleys (Replies: 0)

  2. Newton's Second Law (Replies: 0)

  3. Newtons Laws - Force. (Replies: 0)

Loading...