Magnetic field from a current-carrying slab using Ampère's law

[Saraharris38]

Homework Statement

A thick slab extending from z=-a to z=+a carries a uniform volume current J=J (in the x direction) Find the magnetic field, as a function of z, both inside and outside the slab.

Homework Equations

∫Bdl=(µ0)Ienc

The Attempt at a Solution

I am not sure how to start this. Could someone explain why B is a function of z? Is this just a set-up for the question, or is B obviously a function of z? I also don't really know how to conceptually explain this problem. Thanks!

 

[diazona]

Well, for starters, magnetic field is a thing that exists all throughout space. Different points in space have different values of z. When you specify the value of magnetic field somewhere, you will specify that "somewhere" by giving a value for z (along with values for x and y). Thus B is a function of z.

I'm guessing what you meant to ask, though, was "or is B obviously a non-constant function of z?" But it doesn't say that. B could be independent of z for all you know. (The problem's wording does indeed suggest - but only suggest, not guarantee - that that is not the case.)

To start with, do you understand the meaning of the equation
$$\int \vec{B}\cdot\mathrm{d}\vec{l} = \mu_0 I_\text{enc}$$
? Well enough to conceptually explain it?

If you do, think about what sorts of loops you could draw that might be useful.