Magnetic Fields from Two Infinite Sheets of Current

[pbstriker38]

Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by x_o = 7.5 cm. Each sheet consists of an infinite array of wires with a density n = 19 wires/cm. Each wire in the left sheet carries a current I1 = 3.5 A in the negative z-direction. Each wire in the right sheet carries a current I2 = 3.2 A in the positive z-direction.

What is
$\int^b_a$B⃗⋅dl⃗
where the integral is taken along the dotted line shown, from a to b.



2. Homework Equations
B = uI
B = 1/2 unI



3. The Attempt at a Solution
I used half of $\int$B⃗⋅dl⃗ for the closed loop abcd. Which resulted in "It looks like you've assumed that the integral of B dot dl from a to b is equal to 1/2 of the integral B dot dl around the closed path (abcda). That would be true, for example, if B dot dl at all points along the segment ab were equal to B dot dl at all points along the segment cd. This is not true here. The magnetic field along segment ab is not equal to the magnetic field along segment cd. Further, the orientation of B and dl are different in these two segments, as well. To answer this question, you actually have to do the integral of B dot dl from a to b. "

 

[mfb]

You used a wrong approach, and got a reply why it is wrong.

What is your question?

I think you are supposed to neglect the structure with the individual wires - their precise position is not given anyway. Just approximate the sheets as sheets with continuous current.

 

[pbstriker38]

I don't know what they mean by "do the integral of B dot dl from a to b". What would be Ienclosed?

 

[mfb]

There is no enclosed current in that line.
You can use closed loops for the problem, but you have to choose them carefully.

 

[rude man]

What are the points a, b, c and d in terms of (x,y,z)?

 

[pbstriker38]

I figured it out. It's just the y-component of B(p) * H