A Problem with Two Current-Carrying Wires

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SUMMARY

The discussion centers on the interaction between two current-carrying wires, specifically addressing the forces at play when electrons in both wires move at the same speed. It is established that while the relative velocity of electrons in wires A and B is zero, a magnetic field and force still exist in the lab frame due to the motion of protons in the opposite direction. Additionally, the conversation highlights that thin gauge insulated wires can unintentionally act as antennas, leading to frequency interference in certain applications.

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  • Knowledge of charge density and electrostatics
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Physicists, electrical engineers, and students studying electromagnetism or antenna theory will benefit from this discussion.

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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