Relative magnetic field direction question

1. Jun 10, 2012

ealbers

Sorry for what is probably a silly question....

Lets say we go into deep space, we place a string of electrons along say the X axis...all stationary relative to each other.

Say we place 100 electrons from -50 to +50 using whatever units you want

Now, you start from -50 and travel to 0
I start from +50 and travel to 0

We each indicate to a 3rd observer the orientation of the magnetic field we observe...

Is it true that we would each point in a different direction??

I would see the magnetic field opposite from you?

If so, how would a magnet sitting in the stationary frame of reference of the electrons effect them?

Thanks, again, apologies for a ignorant question

Eric

2. Jun 10, 2012

Staff: Mentor

Yes, the magnetic field is frame variant, both its magnitude and its direction.

No. The magnetic field transforms according to:
$$\mathbf {{B}_{\parallel}}' = \mathbf {{B}_{\parallel}}$$$$\mathbf {{B}_{\bot}}'= \gamma \left( \mathbf {B}_{\bot} -\frac{1}{c^2} \mathbf{ v} \times \mathbf {E} \right)$$

See http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity

3. Jun 10, 2012

ealbers

Please forgive my ignorance on this,

If we would each point a different direction, how would a stationary magnet (relative to the electrons) effect the electrons?

Or would the magnetic fields which we each see not intereact with the stationary (relative to electrons, but not us) magnet?

I guess my real question was,

If a stationary electron has no magnetic field...and a magnet is 'near' it...what happens when my frame of reference is moving? I see a field around the electron, I see a field around the magnet, do they not interact? (Orientation with 2 observers makes me wonder about the direction the electron would move, if it moves)

Thanks
Eric

Last edited: Jun 10, 2012
4. Jun 10, 2012

Staff: Mentor

A magnet which is stationary wrt the electrons would not affect them at all.

In the rest frame of the magnet/electrons it is because the electrons are not moving and therefore there is no magnetic force.

In our frame the moving magnet also makes an electric field which exactly counteracts the magnetic force and leads to no net force on the electrons from the magnet.

5. Jun 10, 2012

ealbers

Ahhh! Thank you!