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

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SUMMARY

The discussion focuses on calculating the magnetic field near a straight current-carrying conductor of finite length L with current I, specifically at a point along the perpendicular bisector at a distance r from the wire. Participants highlight the challenge of applying Ampere’s Law due to the finite length of the wire, suggesting that additional external wiring must be defined to solve the problem. The conversation emphasizes the necessity of considering the wire's endpoints and the implications of extending the wire to infinity for accurate calculations.

PREREQUISITES
  • Understanding of magnetic fields generated by current-carrying conductors
  • Familiarity with Ampere’s Law and its applications
  • Basic knowledge of vector calculus for deriving magnetic fields
  • Concept of finite vs. infinite wire lengths in electromagnetism
NEXT STEPS
  • Study the derivation of the magnetic field due to a finite straight wire
  • Learn about the Biot-Savart Law for calculating magnetic fields
  • Explore the implications of boundary conditions in electromagnetic theory
  • Investigate the use of Ampere’s Law in different geometrical configurations
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Students and educators in physics, electrical engineers, and anyone interested in the principles of electromagnetism and magnetic field calculations.

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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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