Magnetic field of long parallel straight wires

[sweetdion]

Homework Statement

Two infinitely long parallel straight wires carry currents in the +- z direction as shwn in the figure below. Each wire is located on the x-axis a distance of a from the origin.

a) Determine B as a function of y along the line x=0
b) Sketch a graph of B vs. y along the line x=0, including all values of y.

Homework Equations

B=u0I/2PiR

The Attempt at a Solution

for part a i get u0I/PiR
for part b as y increases, B decreases because they're inversely related?

 

[Redbelly98]

Homework Equations

B=u0I/2PiR

The Attempt at a Solution

for part a i get u0I/PiR

Not quite. It looks like you're calculating B at the origin (x=y=0) only, but you need to find B all along the y-axis, as a function of y. So you should get some expression that has y in it.

for part b as y increases, B decreases because they're inversely related?

For this, you'll need to get part (a) done correctly first, then you can sketch the function you get for (a).

 

[sweetdion]

well if one current is flowing in the +z direction and one is flowing in the -z direction the magnetic field is the following:

B=μI/2∏ {[(-y/(x-a)²+y²)+(y/(x+a)²+y²)]ihat + [(x-a/(x-a)²+y²)+(x+a/(x+a)²+y²)]jhat

If we let x equal 0 and reduce, we get B = μIa/∏(a²+y²)

I just know this from the answer in the back of my book, and I have no idea how they get it. :(

From this equation you can deduce the graph. As y goes to infinity it seems as if B goes to zero. Correct?

 

[Redbelly98]

well if one current is flowing in the +z direction and one is flowing in the -z direction the magnetic field is the following:

B=μI/2∏ {[(-y/(x-a)²+y²)+(y/(x+a)²+y²)]ihat + [(x-a/(x-a)²+y²)+(x+a/(x+a)²+y²)]jhat

If we let x equal 0 and reduce, we get B = μIa/∏(a²+y²)

I just know this from the answer in the back of my book, and I have no idea how they get it. :(

How about B due to a single wire, do you know that?

From this equation you can deduce the graph. As y goes to infinity it seems as if B goes to zero. Correct?

Yes.