# Motion in a magnetic field and relativity

1. The problem statement, all variables and given/known data
We’re working in the right-handed Cartesian coordinate system.
Unit system is CGS.
A conducting bar of length L is placed along the x axis. Center of mass at x=0 when t=0.
It’s moving with constant velocity V in the +y direction.
There’s a uniform magnetic field B, such that:
$$\vec B = Bcosβ \hat y – Bsinβ \hat z$$
a. Find the potential difference within the rod. Find the electric field E.
b. Find E’ and B’ in the rod’s frame of reference, far away from the rod. V=0.99c.

2. Relevant equations
Not given, but I assume I’ll need Lorentz force and the relativistic transformation of the fields.

3. The attempt at a solution
Well I think I managed a:
The moving rod’s free electrons are affected by the Lorentz force:
$$\vec F_{mag}=qVBsinβ(-\hat x)$$
This moves the electrons to one side of the rod (the +x side) and the "positive charges" to the -x side. This causes a potential difference and an electrical field E inside the conductor.
The force due to this electric field, at least at some time t1, cancels the magnetic component of the Lorentz force:
$$\Sigma F_x = qE + F_{mag} = 0$$
$$\vec E = VBsinβ \hat x$$
$$\Delta V = ∫\vec E.d \vec s = EL$$

Now for b:
I understand that from a we can see that the bar is basically an electric dipole.
Being an electric dipole, it produces an electric field which I don’t know how to derive.
If I’m to derive this field, with addition to the given B field, I’ll be able to apply Lorentz transformations and get E’ and B’ outside (and far away from) the bar.
What am I missing here?
I’ve got a feeling I’m stuck due to something really dumb.

http://ift.tt/1rx7iuv