# Calculating the magnetic field

1. Oct 30, 2009

### fluidistic

1. The problem statement, all variables and given/known data
A current whose density is $$\vec J$$ circulate through a conductor lattice infinitely long but with a depth $$a$$. The current circulate in a direction which is parallel to the direction in which the lattice is infinitely long.
1)Calculate the magnetic field $$\vec B$$ in a point $$P$$ situated at a distance $$d$$ from the center of the lattice.

2. Relevant equations
Ampère's law I guess.

3. The attempt at a solution
I had a hard time understanding the situation, but I finally think I got it.
However here come my problems. $$\oint \vec B d \vec l = \mu _0 I = \mu _0 \int _S \vec J d \vec S$$, but I don't know what surface I should take as $$S$$.
I've found $$\vec B = \mu _0 \vec J a$$. Which is obviously wrong since I think I should get something like $$\frac{\text{constants}}{r}$$.
Any help is greatly appreciated!

2. Oct 30, 2009

### ApexOfDE

imo, in this case, $$I = J.A = Ja^2$$

From Ampere's law:

$$\oint \vec B d \vec l = B . 2\pi d ==> B = Ja^2 / 2\pi d$$

p/s: im not sure that i understand your problem completely :(

3. Oct 31, 2009

### fluidistic

Thanks for the help. I think the problem is like this : An infinite conductor plane with a depth of $$a$$. The current flows in a direction. I have to calculate the magnetic field inside the lattice (from a depth of $$-\frac{a}{2}$$ if I consider the origin as being just over the lattice) and outside it.
So I don't think that $$\oint d \vec l =2\pi d$$. I'm unsure though.