# Is there magnetic filed or not?

1. Nov 24, 2009

### Ene Dene

1. The problem statement, all variables and given/known data
Suppose that the entire region below the plane z=0 is filled with uniform linear dielectric material of permittivity epsilon. In t=0 a particle of mass m and charge e travels with velocity v in x direction and is parallel with the z=0 plane, and is distance d above the plane. I need to calculate where will the particle fall on to the z=0 plane.

3. The attempt at a solution
Now, I have calculated the force on a particle in t=0 due to bound charge in statical case. I also calculated the bound charge in statical case. Statical case would be if v=0.
What I'm interested in is, if the particle travels with velocity v in x direction, that means that bound charge configuration will follow the particle. In some sense it looks like surface current travelling at velocity v in x direction, right? So my guess is that it will produce a magnetic field in -y direction.
Now, if this is true, then I'm in trouble, I have no idea how to calculate that magnetic field.
Surface current would be:
$$\vec{K}=\sigma*\vec{v}$$
Magnetic field would be in such direction that it would affect the falling of a particle. This bound charge is the result of polarization, It's not really travelling but as particle travels it constantly changes it's configuration, so to me it looks like it's traveling, but does that produce a magnetic field? If so, how do I calculate it, I can't do it by Bio-Savart law since I can't get the B out of the integral.