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Magnetic field of long parallel straight wires

  • Thread starter sweetdion
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  • #1
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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?
 

Answers and Replies

  • #2
Redbelly98
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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).
 
  • #3
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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?
 
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  • #4
Redbelly98
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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.
 

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