Archived Need a guideline for proving/deriving magnetic field from current on a sheet

AI Thread Summary
To prove the magnetic field Hx from a surface current density K, the Biot-Savart Law can be applied, but challenges arise in handling the unit vector aρ. The discussion suggests using Ampere's Law as a simpler alternative to derive the magnetic field equations for z>0 and z<0. The original poster is struggling with the mathematical integration required for the proof. Additionally, there is a correction regarding the variable used in the equations, clarifying that rho should be sqrt(x^2+z^2). The thread emphasizes that this section is for unresolved schoolwork problems, and direct solutions are encouraged.
BlackMelon
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Homework Statement


From the attached picture, I want to proof that Hx=0.5Ky when z>0 and Hx = -0.5Ky when z<0 (Hx is magnetic field caused by surface current density K)
I get stuck with integral problem so my questions are...
1) Can I proof by this Biot-Savart Law?
2) If so, how to eliminate the unit vector aρ or convert it into x or y

Homework Equations


The first equation in the attached picture

The Attempt at a Solution


Look at the attached picture, I was trying to solve but got stuck on math

PS: The problem is at the bottom of the page 192 and 193 of this book:
https://www.mediafire.com/?f0cpqvavy1ddl29
PS2: In the picture, rho should be sqrt(x^2+z^2) not sqrt(x^2+y^2), sorry for the mistake
 

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You can use Ampere's law for an easy solution.
 
Guneykan Ozgul said:
You can use Ampere's law for an easy solution.
Keep in mind that this section of the PF is for old unsolved schoolwork problems. It's unlikely that the OP is still monitoring this thread, or cares about this problem he had so long ago. Feel free to solve problems directly in this section of the PF forums.

Posts in the active Homework Help forums are subject to the normal HH rules, so only hints can be given there. :smile:
 
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