What is the Magnetic Field Near a Straight Current-Carrying Conductor?

AI Thread Summary
The discussion centers on deriving the magnetic field near a straight current-carrying conductor of finite length, specifically at a point along the perpendicular bisector. It highlights the challenge of applying Ampere's Law due to the finite length of the wire, suggesting that external wiring is necessary for a complete solution. Participants propose that one could assume perpendicular wires extending to infinity or consider the wire's ends as connected to infinite continuations. However, this leads back to the use of Ampere's Law, complicating the derivation. The conversation emphasizes the need for clarity on the assumptions regarding the wire's configuration to solve the problem effectively.
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Homework Statement


Find the magnetic field near a straight current carrying conductor of length L and current
I, at a point located along the perpendicular bisector of the wire a distance r from the
wire. Your solution should show all the steps of the full derivation. You cannot use
Ampere’s Law on a finite length wire
 
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A finite length of wire, in order to carry a current, has to have external wiring defined, seems to me. So it seems to me the problem is unsolvable without that extra information.

I suoose you could assume perpendicular wires connected to the wire's end-points and running to infinity.

But by the same token one could run the external wiring as continuations of the wire under question to infinity, in which case we're back to Ampere's law.

If one can assume a finite length of wire carrying a current in some magical way without external wiring then Ampere's law could be used at the wire's mid-point as described.
 

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