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

https://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

 

[sardar]

Your expectation for the first experiment is correct. When two parallel wires carry a current in the same direction, their magnetic fields interact with each other and cause a force of attraction between the wires. This is known as the "right-hand rule" in electromagnetism.

In the second experiment, your expectation is not entirely correct. While it is true that two electrons traveling at the same speed will not experience any relative motion, they will not necessarily behave the same as if they were sitting still. This is because electrons are not just particles, they also have a property called "spin" which determines their orientation in space. When two electrons with the same spin come close to each other, they will repel each other due to the Pauli exclusion principle.

The difference between these two experiments is the presence of a conductor in the first one. Conductors, such as the wires in the first experiment, allow for the flow of electricity and therefore the creation of a magnetic field. This is why the two wires in the first experiment experience a force of attraction. In the second experiment, there is no conductor present, so the electrons cannot create a magnetic field and instead interact through their spin.

In summary, the presence or absence of a conductor is important because it determines whether there can be a flow of electricity and the creation of a magnetic field. Without a conductor, there can be no interaction between electric currents. However, even without a conductor, the spin of electrons can still cause them to interact with each other. This is just one aspect of the complex and fascinating phenomenon of electromagnetism.