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Relativity of Electric and Magnetic Fields

Relativity of Electric and Magnetic Fields
previous home next PDF Michael Fowler, University of Virginia A Magnetic Puzzle… Suppose we have an infinitely long straight wire, having a charge density of electrons of –λ coulombs per meter, all moving at speed v to the right (recall typical speeds are centimeters per minute) and a neutralizing fixed background of positive charge, also of course λ coulombs per meter. The current in the wire has magnitude I = λv (and actually is flowing to the left, since the moving electrons carry negative charge). Suppose also that a positive charge q is outside the wire, a distance r from the axis, and this outside charge is moving at the same exact velocity as the electrons in the wire. What force does the positive charge q feel? The wire is electrically neutral, since it contains equal densities of positive and negative charges, both uniformly distributed throughout the wire (the illustration above is of course schematic). However, since q is moving, it will feel a magnetic force,

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