Magnetic induction of infinite conducting sheet using Ampere's Law

[fatherdaly]

Homework Statement

http://i.imgur.com/j3uzQ.png" to screenshot of question

Homework Equations

The "Integral Form" the question refers to is the http://upload.wikimedia.org/math/0/3/1/0311484f33c932135c09ab12ca8d1a29.png"

The Attempt at a Solution

The hint hasn't really helped me here, and I don't know what path dl should follow. Obviously it should be a rectangle of sorts but then you would have to do it line by line, meaning its not a closed loop. Also, I'm not sure how the thickness comes into it.

 

[G01]

The hint hasn't really helped me here, and I don't know what path dl should follow. Obviously it should be a rectangle of sorts but then you would have to do it line by line, meaning its not a closed loop.

They tell you the path in the problem statement. The path is the perimeter of a rectangle in the x-y plane. Yes, you do have to do the integral line by line, but when you add up the results for each line segment, you still get a closed loop line integral:

$$\oint\vec{B}\cdot d\vec{l}=\int_1 B_1dx + \int_2 B_2dy + \int_3 B_3dx + \int_4 B_4dy = \mu_o I_{enc}$$

HINT: If you consider, using symmetry, the direction of the magnetic field, two of the above integrals should be trivial.

As for the thickness, d: You need the total current enclosed. You are given a current density...