What is the magnitude of the magnetic field B in an infinite sheet of current?

[Punchlinegirl]

An infinite sheet of current, perpendicular to the y-axis is located at y=0. The linear current density \lambda_+_x flows in the +x direction. By inspection, we expect the magnetic field direction B_y, on the positive y side of the sheet to be in the +z direction while the magnetic field on the negative y side of the sheet to be in the -z direction. We choose the Amperican loop as the dashed line with sides of length L and w. The magneto motive force is given by 2LB and the current enclosed is \lambda_+_x * L.
Let L=0.5 m, w=0.078 m, \lambda_+_x= 1.89 A/m. Find the magnitude of the magnetic field B. Answer in units of T.

I really have no idea how to do this problem. Can someone help? Thanks

 

[siddharth]

Hint: Ampere's Law.
Read the question again. Towards the end of the question, there is a big hint given on what closed loop to take.

 

[Punchlinegirl]

Ok so the loop I use has sides L and W.
I know that Ampere's Law says B*ds*cos theta= \mu*I
So to get B I divide \mu *I by 2L+2W since you use the perimeter of the square.
So its (1.25e-6)(0.5)(1.89)/ (2*0.5)+(2*.078)

Am I going about this in the right way?

 

[siddharth]

I advise you start over from the beginning.

Fist, draw the sheet, the current, the field direction above and below, and the closed amperian loop.

Now, when you integrate over the closed loop, you will be able to see what part contributes to the integral and what part doesn't.