Magnetic field between two long straight wires

[cjbreen]

Hi. Any help on this problem would be greatly appreciated. Here is the problem:
A)Determine the magnetic field between two long straight wires at a point 0.500cm from the left wire when the two wires are 3.00cm apart in terms of the current I1 (left wire) when the other (right wire) carries I2=10.0A. Assume these currents are in the same direction and draw a picture. Use a + to indicate into the plane of the page, and a – to indicate out of the plane of the page. B)Repeat, but with the currents in opposite directions and draw a picture. C)If I1 =15.0A, what is the value obtained for magnetic field in part (A)? What is the value obtained for magnetic field in part (B)? D) At what position will the magnetic field from (C) be equal to zero?

I was using the equation BT=(?0I1)/(2?r1) + (?0I2)/(2?r2)

For part B would it be BT=(?0I1)/(2?r1) - (?0I2)/(2?r2) since the currents are in opposite directions or am I mixing up what part should be added and which one should be subtracted?

I also always get confused when figuring out if its into the plane of the paper or out of the plane of the paper. Is there an easy way to remember that? And I don’t have a clue how to figure out part D. Do I use the same equation? If so how do I manipulate it since there are 2 wires(radius)?

Thank you so much to anyone who is willing to help. I really appreciate it.

 

[cjbreen]

Okay, I just realized that my equation didn't copy right, apparently the symbols from word didn't transfer. The equation I used was (mu0 * I1)/(2pi * r1) + (mu * I2)/(2pi * r2). I'll go ahead and attach the word document I wrote the question in incase that's clearer to read. For future reference is there something special I should use so that the formulas with special characters transfer right? Thanks again!

 

[rootX]

Can you apply rule of superposition here?
Like you do with electrical field?

 

[Weimin]

Part A: same direction==>B=B1-B2

The net vector will point inward or outward depending on the strengths of two fields. So you need to find where two fields cancel each other (it's a line on the plane). The sign will change when crossing this line.

Part B: different directions==>B=B1+B2

The sign keeps unchanged between two wires.

 

[cjbreen]

Thanks to you that helped. But I'm still stuck on part D. How do I set it up to determine if where it is zero. I really don't have a clue on where to go for that part. Thanks!

 

[nrqed]

Thanks to you that helped. But I'm still stuck on part D. How do I set it up to determine if where it is zero. I really don't have a clue on where to go for that part. Thanks!

First, draw the directions of the B fields in all the regions (for points between the wires, to the left of the first wire, to the right of the second wire). In what region(s) are the two B fields opposite? Now, is it possible for the *magnitudes* of the two B fields to be equal in the regions where the two B fields are opposite? (Hint: the two magnitudes will be equal only if the point is closer to the smaller current). If the answer is yes, just set up an equation imposing that the two magnitudes are equal,
$$\frac{\mu_0 I_1}{2 \pi r_1} = \frac{\mu_0 I_2}{2 \pi r_2}$$
where r_1 and r_2 are the distances from the point to the two corresponding wires (these are not independent, you may write an equation relating the two if you know the distance between the two wires)

 

[cjbreen]

Thanks so much, I wasn't even thinking about an equation relating the two distances since I do know the distance between them, I'm such a space case sometimes. Thanks again.