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.