Magnetic Field from Sheets of Current

[typeinnocent]

Homework Statement

Two infinite sheets of current flow parallel to the y-z plane. The left-hand sheet, which intersects the x-axis at x = 0, consists of an infinite array of wires parallel to the z-axis with a density n = 990 wires/m and a current per wire of IL = 0.19 A in the +z direction. The right-hand sheet, which intersects the x-axis at x = a = 10 cm, is identical to the left-hand sheet, except that it has a current per wire of IR = 0.19 A in the -z direction.
https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2112/summer/homework/Ch-26-B-Force-and-Fields/B-field-from-sheets/0805.gif
Calculate the y-components of the net magnetic field at x = 5 cm

Homework Equations

Ampere's Law: $$\mu$$o*I/(2*pi*r)

The Attempt at a Solution

I thought I would only have to use Ampere's Law for each sheet, so my equation looked like this:
B = $$\mu$$o(.19)/(2*pi*.05)
I multiplied this answer by two, since they have the same current and are the same distance away, but the solution was incorrect.

Any suggestions?
My only guess is that I'm treating it like a line rather than a sheet, but even if you take dB, it turns out to be the same equation.

Thanks in advance!

 

[flatmaster]

B = 0
Look for symetry. I'll explain more later. Must sleep.

 

[nlightner]

Hello,

Thank you for your question. In order to calculate the y-component of the net magnetic field at x = 5 cm, you will need to take into account the contributions from both sheets of current. Since the sheets are parallel to each other, the magnetic fields they produce will add together in the y-direction.

To calculate the magnetic field from each sheet, you can use the equation you mentioned, Ampere's Law, but you will need to integrate over the entire sheet rather than just one wire. This will give you the total magnetic field at any given point in the y-z plane.

Once you have the magnetic field from each sheet, you can add them together to find the net magnetic field at x = 5 cm. Remember to take into account the direction of the magnetic field from each sheet, as one is in the +z direction and the other is in the -z direction.

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!

Best,