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

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Ampere's Law can be applied to a long thick slab by considering the current density J in the x direction. The confusion arises in calculating the line integral of the magnetic field B around the Amperean loop, specifically why it is represented as BL instead of B(2L). The key point is that only the sections of the loop outside the slab contribute to the integral, leading to the simplified expression. A diagram illustrating the slab and the Amperean loop would clarify the situation further. Understanding these concepts is crucial for mastering electromagnetism, especially during finals.
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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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