Help me understand electromagnetism.

[mrspeedybob]

Here are two hypothetical experiments to illustrate my confusion...

#1
Two wires are positioned parallel to each other. A current is applied to both wires in the same direction. I would expect the 2 currents to each generate a magnetic field and that the 2 fields would interact to produce a force pulling the wires towered each other.

#2
Two electron guns fire electrons 1 by 1 simultaneously along parallel trajectories. Since each electron is going at the same speed there is no relative motion between them, they should behave the same as if they were sitting still. If they were sitting still then they should repel each other.

Do I have the correct expectation for each of these experiments? If not, what is my error. If so then the only difference I see between these 2 experiments is the presence or absence of the conductor. Why does this matter?

[Dr Lots-o'watts]

In 1., there is no electric field. It is balanced out by the metallic atoms of the wire. Only the magnetic field can be observed.

[Chronos]

EM fields do not interact with each other. Their effects are only exerted on matter.

[Bob S]

Your two hypothetical experiments propose very interesting and important electromagnetic problems in charged particle beams.

#1 has already been answered. There is only an attractive magnetic force.

#2 has both the attractive magnetic force between the two beams (actually between the magnetic field of one beam and the Lorentz force on individual moving charges in the other) and the repulsive Coulomb forces (between the charge per unit length in one beam and individual charges in the other). When transforming from the lab frame into the center of mass frame where the charges are motoinless, the attractive magnetic forces become attractive Coulomb (E = q(v x B)) forces.

In this second case, the repulsive Coulomb force is always larger than the attractive magnetic force. But when the beams become extremely relativistic, the two opposing forces cancel. See my post #5 and attachments in

http://www.physicsforums.com/showthread.php?t=405055

These two opposing forces also exist within single high-current charged-particle beams. For intense proton beams with very low beam size and low divergence (low "phase space"), preventing the Coulomb forces from blowing the beam size up before the beam becomes relativistic is an important aspect of particle accelerator design.

Bob S