How does Ampere's Law apply to a long thick slab on the z axis?

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SUMMARY

The discussion focuses on applying Ampere's Law to a long thick slab oriented along the z-axis with a current density J directed in the x direction. The user struggles to understand why the integral of the magnetic field B along the Amperian loop results in BL instead of B(2L), despite two sides of the loop being within the slab. The conversation emphasizes the importance of visualizing the problem with diagrams and clearly defining the Amperian loop to facilitate comprehension.

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  • Ampere's Law and its mathematical formulation
  • Understanding of magnetic fields and current density
  • Familiarity with the concept of Amperian loops
  • Basic knowledge of electromagnetic theory
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  • Learn how to visualize magnetic fields using diagrams
  • Explore the derivation of magnetic fields in slabs and cylinders
  • Review examples of calculating magnetic fields using Amperian loops
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This discussion is beneficial for physics students, particularly those studying electromagnetism, as well as educators seeking to clarify concepts related to Ampere's Law and magnetic fields.

Kvm90
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Hey all- I'm a Junior in college, pretty much have Ampere's law down except there's always been one thing I don't quite understand and have just memorized.

Say you have a long thick slab from -z to z on the z axis. J= J in the x direction. Find the B field in and out of the slab.

My attempt:

Use amperes law. I understand the RHS 100%, simple. On the LHS, however, I can't understand why int(B.dl) is BL rather that B(2L). Two sides of your Amperean loop are within the slab so why is int B.dl just BL.

Quick help would be appreciated; finals week- ugh!
 
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If anyone can help tonight that would be great; is my question unclear?

I really want to fill this gap in my understanding of the basics of E&M
 
I'm struggling to understand exactly what you mean by "long thick slab from -z to z on the z axis", perhaps a diagram would be helpful. Drawing your amperian loop on the diagram and explicitly writing out both sides of the equation you are trying to understand would make it even easier to help.
 

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