Magnetic field of a plane with a current going through it There's something I just cant understand about the application of Ampere's Law for a plane with current going through it.
While every book and my proffesor says it is (and therefore im sure its is correct):
$$B= \frac{\mu_0NI}{2l}$$
I think it should be:
in x) $\frac{\mu_0nI}{l}$
in -x) $\frac{\mu_0nI}{l}$
I understand the idea of superposition of fields, but yet I don't understand why would you add the fields in the x and -x directions so freely.
It's not like the magnetic field in the -x direction is also present all through the z direction. 
So, what I'm triyng to ask is, why isn't the field defined as the same, but in opposite direction and is instead summed ?

 A: According to Biot Savart's Law the magnetic field should be perpendicular to the current. Since the current is in the $ \hat{x} $ direction the magnetic field is at first pass in either the $ \hat{y} \text{ or } 
\hat{z} $ direction. Getting the actual direction is a bit tricky because you have to use the symmetry you have cleverly. Pick an infinitesimal line of the sheet for fixed $z$  and $y$ . The magnetic field loops around it. Convince yourself that the $ \hat{z}$ component is canceled out but by another piece of wire at same $z$ but negative $y$. Then next convince yourself that above the sheet the magnetic field points in $-\hat{y}$  and below points in $\hat{y}$. Now draw your amperian loop. The line element direction match up with magnetic field direction so that above the sheet we have $BL$ (both have negative directions) and below we have $BL$ (both have positive directions). There are other two pieces but they give no contribution. Then you should be able to move on from there.
