A Magnetic Puzzle

A Magnetic Puzzle - into the page where the charge is...

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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). So q feels no electrical force. However, since q is moving, it will feel a magnetic force, The magnetic field lines are vertical circles centered along the axis of the wire, the field being
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Unformatted text preview: into the page where the charge is (remember the current is to the left) and of magnitude so the force on the charge is of magnitude and is directed away from the wire, so the charge will accelerate away from the wire. Now let us examine the same physical system in the frame of reference in which the charge is initially at rest. In that frame, the electrons are also at rest, but the positive background charge is flowing at v : What force does q feel in this frame ? Since q is at rest, it cannot feel a magnetic force: such forces depend linearly on speed! Yet it looks as if it cant feel an electric force either, because the positive and negative charges in the wire have equal densities, right? This leads to the conclusion that q feels no force at all in this frame, so it wont accelerate away from the wire, as it did in the other frame. This is of course nonsenseso where did we go wrong?...
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A Magnetic Puzzle - into the page where the charge is...

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