Why Is the Magnetic Vector Potential Azimuthal Inside an Infinite Solenoid?

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SUMMARY

The magnetic vector potential inside an infinite solenoid is azimuthal due to the symmetry of the magnetic field generated by the solenoid. The formula A(𝑟) = ∫𝑣 (𝑗(𝑟′)/𝑟) dτ is not applicable because of the infinite extent of the current. Instead, the magnetic field B can be determined using the integral form of Ampere's Law, and the vector potential A can be deduced by recognizing that B = Curl(A). This approach simplifies the calculation of A in the context of an infinite solenoid.

PREREQUISITES
  • Understanding of magnetic vector potential and its significance in electromagnetism
  • Familiarity with Ampere's Law and its integral form
  • Knowledge of vector calculus, specifically the Curl operator
  • Concept of symmetry in magnetic fields, particularly in solenoids
NEXT STEPS
  • Study the derivation of the magnetic field inside an infinite solenoid using Ampere's Law
  • Explore the mathematical properties of the Curl operator in vector calculus
  • Investigate the physical implications of magnetic vector potential in different geometries
  • Learn about the applications of magnetic vector potential in advanced electromagnetism
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Physicists, electrical engineers, and students studying electromagnetism who seek to deepen their understanding of magnetic fields and vector potentials in theoretical and practical applications.

pardesi
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Why is the magnetic vector potential of a point inside a infinite soleniod azimuthal assuming the axis of solenoid is the z axis.
Problem is the formulae [itex]A(\vec r)=\int_{v} \frac {\vec J(\vec r^{'})}{r} d\tau[/itex] doesn't hold any more due to the infinite extent of the current
 
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When you say "why is" I assume you mean "what is", and A is simple to find in this case because you can find B using the integral form of ampere's law and then guess A by looking at B = Curl(A).
 

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