Solve Ampere's Law Problem for Uniform Current Density

[Crazy Gnome]

Homework Statement

A conducting slab of thickness a is bounded by the planes z= $$\pm$$a/2 and carries a uniform current density J=J (y hat)

Use the integral form of Ampere's law to to find magnetic field everywhere
2. Relevant equations

Integral for of Amperes law: Integral (B \bullet ds) = \mu ₀ J_enclosed

The Attempt at a Solution

All of the examples in class and in the book use cylindrical symmetry so I was a bit perplexed as how to approach taking an integral over a closed path dotted into a B in cylindrical coordinates.

 

[Redbelly98]

Try using a rectangular loop for the integration. Each leg of the loop is either perpendicular or parallel to B.