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Question 07/02 CURRENT IN A WIRE



In freshman physics we are told that a current in an "infinite"
cylindrical wire flows with constant density J independent of this
distance from the center of the wire. But we also learn how to use
Ampere's Law to calculate the magnetic field in the wire. Doesn't the
magnetic field act to make the current density non-uniform?

Answer: 11/02 The Hall Effect explains this question. A charge moving in
a magnetic field experiences a force perpendicular to its velocity and
to the magnetic field. Charges moving in a wire will shift to one side
of the wire producing a charge separation. This charge separation gives
rise to an electric field. The charge continues to shift until the
force of the electric field exactly balances the magnetic force. Then
the current continues straight on, since the two forces exactly cancel.
Inside a wire carrying a uniformly distributed current, the Hall Effect
generates a small radial electric field that exactly cancels the
influence of the magnetic field produced by the current thus
maintaining the uniform distribution of current in the wire.

Another way to see this recognizes that magnetic effects come from
considering moving charges relativisticly. For example, currents moving
in the same direction in two parallel wires will experience relativistic
electrostatic effects. The positive and negative charges in one wire
look over at the other wire, seeing electrons moving. Relativity says
that moving objects appear shorter, so the moving electrons appear
closer together (their distance of separation appears shorter) and their
density looks larger. This apparent increase in negative charge density
causes an attraction to the positive charges in the first wire. But
since the negative charges in the first wire move in the same direction
at roughly the same speed at those in the second wire, no relativistic
density increase occurs (no relative velocity = no length decrease = no
density increase = no net force). Since all the electrons in the
uniformally distributed current move at roughly the same drift velocity
in the wire, they experience no magnetic force due to their own motion
because there is no relative motion among them.

This nonuniform current distribution actually does occur when no wire
confines the charge flow. In a plasma, moving charge sets up a magnetic
field that generates an attraction among the parts of the current,
giving rise to the magnetic pinch effect.

Your comments would be appreciated.

Prof. Eric T. Lane 318 Grote Hall 423-425-4523 eric-lane@utc.edu
Physics Dept.2352, University of Tennessee at Chattanooga, TN 37403

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.