Magnetic field using Biot-Savart's Law

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SUMMARY

The discussion focuses on using Biot-Savart's Law to determine the magnetic field at the center of an infinitely long hollow cylinder carrying a constant current I. It is established that the magnetic field at this point is zero due to symmetry, as the contributions from an infinite number of current-carrying wires on the cylinder's surface cancel each other out. The discussion highlights that while Ampere's Law is often preferred for such problems, Biot-Savart's Law can effectively demonstrate the same conclusion through symmetry arguments.

PREREQUISITES
  • Understanding of Biot-Savart's Law
  • Familiarity with magnetic fields generated by current-carrying conductors
  • Knowledge of symmetry in physics
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the application of Biot-Savart's Law in various geometries
  • Learn about Ampere's Law and its applications in calculating magnetic fields
  • Explore the concept of magnetic field symmetry in current-carrying systems
  • Investigate the effects of different current configurations on magnetic fields
USEFUL FOR

Physics students, educators, and anyone interested in electromagnetism, particularly those studying magnetic fields generated by current-carrying conductors.

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Homework Statement



An in finitely long hollow cylinder of radius a carries a constant current I. Use Biot-Savart's law
and show that the magnetic field at the centre of the cylinder is zero.

Homework Equations



Biot-Savart's law

The Attempt at a Solution



I cannot seem to come up with anything meaningful. I have tried searching this question but it seems the best way is normally to use Ampere's law and not Biot-Savarts law. Could someone explain the steps or show the steps how we could use Biot-Savart's law in this case.
 
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This is really just a symmetry argument. Think about sitting between two wires that have current flowing in the same direction. You know the magnetic field from one wire (using the Biot-Savart law), and you know it is going to cancel that of the other wire in the middle. Now just line the surface of a cylinder with an infinite number of these wires and you have your problem, but you get the same result.
 

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