How Does Current Affect Magnetic Fields in and Around a Wire?

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SUMMARY

The magnetic field around a long, current-carrying wire can be determined using Ampère's Law and the Biot-Savart Law. Inside the wire, the magnetic field is proportional to the current density, while outside the wire, it follows the formula B = (μ₀I)/(2πr), where μ₀ is the permeability of free space. The discussion emphasizes the importance of considering current elements on opposite sides of the wire to understand their contributions to the overall magnetic field. This analysis is crucial for accurately calculating magnetic fields in electromagnetic applications.

PREREQUISITES
  • Understanding of Ampère's Law
  • Familiarity with the Biot-Savart Law
  • Knowledge of magnetic field concepts
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the derivation of Ampère's Law in cylindrical coordinates
  • Learn about the applications of the Biot-Savart Law in complex geometries
  • Explore the effects of varying current on magnetic fields
  • Investigate the relationship between magnetic fields and electromagnetic induction
USEFUL FOR

Physics students, electrical engineers, and anyone interested in understanding the principles of electromagnetism and magnetic field calculations around current-carrying conductors.

Master J
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A long, current carrying wire has a radius R and current I.
What is the magnetic field inside, and outside the wire?


Now, if it asked what is the field a distance r from the wire, I could simply use the Law of Biot & Savart (mu.I/2.pi.r). I havn't dome electricity in a while and I am stuck on this one.

I am sure its simple, I just need a nudge.

Thanks guys.
 
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Where will the current elements be carried on the wire? And as they are in motion consider the current elements on opposite sides of the wire and what their contribution would be to the field within the wire.
 

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