Vector Potential: Finding the Vector Potential of a Long Wire

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SUMMARY

The discussion focuses on determining the vector potential of a long wire, given the magnetic field B-field = (\muI)/(2\pir). The user seeks to understand the relationship between the magnetic field and the vector potential, specifically through the equation \nabla X A. It is established that the magnetic field has only an azimuthal component, indicating that the vector potential A will consist of radial and axial components.

PREREQUISITES
  • Understanding of vector calculus, particularly curl operations.
  • Familiarity with magnetic fields and vector potentials in electromagnetism.
  • Knowledge of the Biot-Savart Law and its applications.
  • Basic concepts of cylindrical coordinates in physics.
NEXT STEPS
  • Study the derivation of the vector potential for cylindrical geometries.
  • Learn about the Biot-Savart Law and its implications for magnetic fields.
  • Explore the mathematical properties of curl and divergence in vector calculus.
  • Investigate applications of vector potentials in electromagnetic theory.
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism who need to understand the relationship between magnetic fields and vector potentials.

germx
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Hello all. I am hoping someone could lend a hand. I need to determine the vector potential of a long wire. I am given the B-field = ([tex]\mu[/tex]I)/(2[tex]\pi[/tex]r) and I know at some point I will need to use [tex]\nabla[/tex] X A. Thanks in advance.
 
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What's the equation of [tex]\bar{B}[/tex] in terms of [tex]\bar{A}[/tex]?

The magnetic field runs in rings around the conductor, so it only an azimuthal component.
This tells you that the A field generating B will be limited to radial and axial components.
 
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