Calculating Magnetic Fields in Cylinders w/ Currents

AI Thread Summary
The discussion focuses on calculating the magnetic field around two infinitely long cylinders with specified current distributions. The user successfully applied Ampere's law to find the magnetic field for the region where r is less than a, resulting in H = (Jo r squared)/3a. However, they express confusion regarding the integration limits and the method for determining the magnetic field in the regions where a is less than r less than b and r is greater than b. Clarification on these calculations and the addition of magnetic fields is requested. The thread highlights the challenges of applying theoretical concepts to specific scenarios in electromagnetism.
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Homework Statement



Consider two infinitely long cylinders with radius a and b and currents:

J =

(Jo r)/a for r less than a

-Jo for a less than r less than b
Find the magnetic field in

1) r less than a

2) a less than r less than b

3) r greater than b

Homework Equations


The Attempt at a Solution



I think I was able to compute the magnetic field for r less than a

using Ampere's law

H 2 pi r = (the integral from 0 to a of) (Jo r) /a 2 pi r dr the result that I found for H was H = (Jo r squared )/3aIn the other cases I am confused about the integration limits and the addition of magnetic fields.
How can I find the magnetic field for a less than r less than b, and for r greater than b ?I would appreciate some help, thanks a lot.
 
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Can anyone give me an idea how to solve this please? I ll truly appreciate it.
 
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