A Problem with Two Current-Carrying Wires

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The discussion centers on the interaction between two current-carrying wires, highlighting the apparent contradiction of force generation despite electrons moving at the same speed. In the lab frame, a magnetic field and force exist, while in the electrons' frame, these are absent, yet protons moving in the opposite direction create a net electrostatic force. Additionally, the differing charge densities in the electrons' rest frame contribute to this force. Participants also noted that thin insulated wires can unintentionally act as antennas, leading to frequency issues in specific applications. This highlights the complexity of electromagnetic interactions in various reference frames.
Radek Vavra
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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?
 
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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.
 
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.
 
They also discovered that a pair of wires of thin gauge (insulated) will accidentally become an antenna and cause frequency problems in certin applications.
 
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