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fysicsandphol
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E & M Magnetism Relativity "Paradox"
In theory the laws of magnetism are derivable from coulomb's law and special relativity. Right. While my physics homework group were doing a problem set, I came up with this seeming paradox. (This isn't a homework question). There are 2 senarios:
Senario 1:
The stationary lab frame is that of a positive charge. We'll call this p.
Some distance above p there is a theoretical wire with an equal amount of positive ions and electrons flowing in opposite directions with a velocity v relative to p.
Senario 2:
An equivalent way of stating this is that there is a wire with electrons moving with speed u (where u is just the relative velocity of the electrons in the frame the positive ions). The positive ions are stationary (The lab frame is that of the + ions). At point p there is a positive charge moving with speed v parallel to the wire.
It is obvious that these are qualitativly the same scenario from 2 reference frames.
In scenario 2, it is obvious that since the wire has a current, it creates a magnetic field B. Since the charge at p is moving, this implies there is a magnetic force on particle at p pointing either up, or down.
Using only coulomb's force and the laws of relativity, derive the magnetic force on the particle at p in scenario 2?
This isn't a real paradox. But it seems counter-intuitive because of the parity between the positive flow and the negative flow in case 2.
Senario 1:
The stationary lab frame is that of a positive charge. We'll call this p.
Some distance above p there is a theoretical wire with an equal amount of positive ions and electrons flowing in opposite directions with a velocity v relative to p.
Senario 2:
An equivalent way of stating this is that there is a wire with electrons moving with speed u (where u is just the relative velocity of the electrons in the frame the positive ions). The positive ions are stationary (The lab frame is that of the + ions). At point p there is a positive charge moving with speed v parallel to the wire.
It is obvious that these are qualitativly the same scenario from 2 reference frames.
In scenario 2, it is obvious that since the wire has a current, it creates a magnetic field B. Since the charge at p is moving, this implies there is a magnetic force on particle at p pointing either up, or down.
Using only coulomb's force and the laws of relativity, derive the magnetic force on the particle at p in scenario 2?
This isn't a real paradox. But it seems counter-intuitive because of the parity between the positive flow and the negative flow in case 2.