A Problem with Two Current-Carrying Wires

[Radek Vavra]

We all know that there is a force between them. But I wonder... if electrons in both wires are moving with the same speed the relative velocity between the electrons in wire A and B equals zero - but then there would be no magnetic field and no force. Could you help me with this?

 

[mfb]

There is a magnetic field and a force in the lab frame. In the frame of the electrons, there is not - but then you have protons moving in the opposite direction.

 

[jtbell]

Also, in the electrons' rest frame, the positive and negative charge densities are different, so there is a net electrostatic force in addition to the magnetic force between the protons.

 

[Introyble]

They also discovered that a pair of wires of thin gauge (insulated) will accidentally become an antenna and cause frequency problems in certin applications.

 

[sardar]

Thank you for bringing up this interesting question. You are correct that two current-carrying wires will experience a force between them due to the magnetic fields created by the moving electrons. However, the relative velocity between the electrons in wire A and B does not necessarily have to be zero for this force to exist.

The force between the wires is actually due to the interaction between the magnetic fields created by the moving electrons. When the electrons in wire A are moving, they create a magnetic field around the wire. Similarly, the electrons in wire B also create a magnetic field. These two magnetic fields interact with each other, resulting in the force between the wires.

Even if the electrons in both wires are moving at the same speed, their magnetic fields are still interacting with each other. This is because the direction of the current in each wire is opposite, causing the magnetic fields to also be in opposite directions. This results in a force between the wires, regardless of the relative velocity between the electrons.

I hope this helps to clarify the concept. Keep asking questions and exploring the wonders of science!