How Does Ampere's Law Apply to an Infinite Sheet of Current?

[babydimples]

Homework Statement

Consider an infinite sheet of parallel wires. The sheet lies in the xy
plane. A current I runs in the y-direction through each wire. there are
N/a wires per unit length in the x direction. Write an expression for B(d)
the magnetic field a distance d above the x y plane of the sheet and we
have to express the magnetic field as a vector.

Homework Equations

Ampere's Law --> closed integral of (Bdl) = uIencl

The Attempt at a Solution

I know that by using the right hand rule, the magnetic field would
pointing in the negative x direction if i pick a point above the surface.
Then I tried to figure out what Iencl is and I get I = (N/a)(a)(I) = NI
Then using ampere's law I get

B(top integral + bottom integral) = uNI
B(2a) = uNI
B= UNI/2a
and since the magnetic field is heading towards the negative x direction
I typed in B = -(uNI)/2a x


Please help! I don't know what I'm doing wrong! Thanks!

 

[kuruman]

I typed in B = -(uNI)/2a x

The magnetic field is in the positive x-direction above the xy plane and in the negative x- direction below the xy plane. Its magnitude does not depend on x. Maybe the x in your equation was meant to be a unit vector but that's not how it will be interpreted by anyone who reads it, including a machine.