The field due to multiple concentric solenoids with water

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SUMMARY

This discussion focuses on calculating the magnetic field strength generated by a system of 13 concentric solenoids, utilizing the Faraday effect. The magnetic field is determined primarily by the innermost solenoid, as indicated by Ampere's Law, which simplifies the calculation to B = μ ninner I. The presence of water layers between the solenoids serves to cool the wires, but for the purpose of this calculation, the medium is assumed to be a vacuum. The effective current seen from the center is 13I, due to the cumulative effect of the solenoids.

PREREQUISITES
  • Understanding of Ampere's Law and its application in magnetic field calculations
  • Familiarity with the Faraday effect and its relevance in electromagnetic studies
  • Knowledge of solenoid configurations and their magnetic properties
  • Basic principles of electromagnetism, including magnetic field strength equations
NEXT STEPS
  • Explore advanced applications of Ampere's Law in complex magnetic systems
  • Investigate the effects of different core materials on solenoid magnetic fields
  • Learn about the thermal management techniques for solenoids in high-current applications
  • Study the implications of the Faraday effect in optical systems and materials
USEFUL FOR

Students and researchers in physics, electrical engineering, and anyone involved in the design and analysis of electromagnetic systems, particularly those working with solenoids and magnetic fields.

Jeremy_W
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Homework Statement


OK, so I am doing research this semester and I am working with the Faraday effect. For my magnetic field, we are using a large solenoid that is comprised of 13 concentric solenoids each of which has the same number of coils per unit length. In between each of these layers there are layers of water to cool the wires to prevent overheating and of course in the middle is the substance which the light will pass through. However, for this calculation, I will assume it to be a vacuum (under the instruction of the professor). So I need to calculate the magnetic field strength.

Homework Equations


Ampere's Law: ∫B.ds=μOJ
Magnetic Field of one solenoid with a non-vacuum core: B = μnI

The Attempt at a Solution


Well, I read in another thread that the magnetic field in the center is simply the magnetic field due to the inner most one. And when I use Ampere's Law, I get the same thing. So basically, I am getting:

B = μ ninner I
 
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If B is just due to the most inner one, then throw away the other solenoids :biggrin:
Imagine that all the solenoids have nearly the same radius, then if you stand in the center, what you see is one solenoid with current 13I, not I.
 

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