Why does two parallel currents attract each other when two proton beams repel each other?
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The current carrying wires are repelled by Lorentz force while photons repel each other with electrostatic force. The two cases are not similar. – Sam Feb 23 '20 at 03:50
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Related: Do two cathode rays attract each other? – Vishnu Feb 23 '20 at 04:12
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The wires carring a current are effectively electrically neutral (equal numbers of positive and negative charges) so the dominant force between the moving charges in the magnetic field produced by the other charge is the attractive Lorentz force.
When you have just beams of protons they are also subjected to the electrostatic repulsive force which is much stronger than the attractive Lorentz force and so there is net repulsive force between them.
Farcher
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2Is there a relativistic speed at which for to proton (or electron) beams the Lorentz force will be stronger the electrostatic force? – HolgerFiedler Jul 11 '17 at 08:41
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1@HolgerFiedler In the rest frame of the protons there is only electrostatic force. – Keith McClary Jul 11 '17 at 21:35
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Thats because in one case you have a wire and in the other case you don't. I.e. the wire situation is electrically neutral if the current stops flowing. Have a look at the nice youtube video. In the free proton case its just electric repelling force.
mikuszefski
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