(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Lorentz force and Newton's law

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**