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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]


    [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
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