Magnetic field of plane with thickness d with uniform surface current

[SherlockHolmie]

Homework Statement

Find the magnetic field due to an infinite plane of thickness d (i.e. an infinite box) that carries current with uniform surface current density j.

Relevant Equations

$\oint \vec B \cdot \vec dl = µ_0 I$

I'm confused what's meant by a uniform surface current density since this plane has a thickness, It would need a current density distributed through its cross sections, I thought.Edit: I tried solving with proper LaTeX and all my steps, but it looked awful. For outside, I got B=µ_0jd/2.
for inside, I got d'jµ_0 where d' is the height of the smaller amperiant loop.

 

[kuruman]

I'm confused what's meant by a uniform surface current density since this plane has a thickness, It would need a current density distributed through its cross sections, I thought.

You thought correctly. Your relevant equation needs fixing before you use it.

 

[SherlockHolmie]

You thought correctly. Your relevant equation needs fixing before you use it.

I said BL because I didn't know how to write loop integral in the relevant equations. Thank you!

 

[kuruman]

I said BL because I didn't know how to write loop integral in the relevant equations. Thank you!

You would be served well if you taught yourself how to use LaTeX and write equations like $$\oint\vec B\cdot d \vec l=\mu_oI_{encl.}$$Click on the "LaTeX Guide" link, bottom left corner above the "Attach files" link to get started.

 

[SherlockHolmie]

You would be served well if you taught yourself how to use LaTeX and write equations like $$\oint\vec B\cdot d \vec l=\mu_oI_{encl.}$$Click on the "LaTeX Guide" link, bottom left corner above the "Attach files" link to get started.

Ah, ok. I didn't know I needed to put ## between my LaTeX on here. I'll use that in the future. Appreciate it!