Ampere's Law for current carrying wire

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Ampere's Law is applied to derive the magnetic field inside a current-carrying wire, leading to the equation B = (1/2)μJr, where J represents the constant current density. The discussion highlights that the integral ∫B*ds equals μI, with the angle θ being zero, simplifying the equation. Participants clarify that r refers to the radius of the wire, not its length, and that J is the current per unit cross-sectional area. The integration limits are suggested to be from 0 to 2π, treating the wire as a cylinder. The conversation emphasizes the need to substitute I with J for accurate calculations.
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Homework Statement



Use Ampere's Law to show that the equation for the magnetic field inside a current carrying wire is (1/2)μJr where J is the current density (assumed constant).


Homework Equations



∫B*ds=μI

The Attempt at a Solution



∫B*ds=μI

B*ds=B(ds)cosθ I think θ is 0 in this situation?

∫Bds=μI I believe r is length. If so would I=Jr?

∫Bds=μJr

From here I don't know what to do. What would my limits of integration be?
 
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hi btpolk! :smile:
btpolk said:
I believe r is length. If so would I=Jr?

no, r is radius

and J is the current per cross-section area
 
That said, I'm guessing I would treat the wire as a cylinder and the limits of integration would be 0 to 2pi? Also where does the J come in? Would it be some kind of substitution for I?
 

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