Where is the magnetic field zero between two antiparallel current-carrying wires

[nerdy_hottie]

Homework Statement

Consider two parallel conducting wires along the direction of the z axis as shown below. Wire 1 crosses the x-axis at x = -2.60 cm and carries a current of 2.00 A out of the xy-plane of the page. Wire 2 (right) crosses the x-axis at x = 2.60 cm and carries a current of 6.80 A into the xy plane.
At which value of x is the magnetic field zero? (Hint: Careful with sign)

Homework Equations

B=μ_oI/2∏a

The Attempt at a Solution

I am guessing that the field will equal zero at some point to the left of the left wire.
I have tried this:
0=μ_oI₁/2∏(x+0.026m) + μ_oI₂/2∏(x+0.052m)
I make one of these expressions negative because they are in opposite directions, then I bring one expression to one side and the signs on both expressions are now both positive again. Filling in my numbers, and rearranging I get 6.8x+0.1768=2x+0.104, and x=-0.0728m.
I then add the positive equivalent of this number to 0.026m and take into account the value is on the negative x-axis to get -0.0412m.

I have a feeling that I am going wrong somewhere with the sign of something.

 

[BruceW]

Filling in my numbers, and rearranging I get 6.8x+0.1768=2x+0.104, and x=-0.0728m.

I think the equation is right, but the value for x isn't right. Also, you've used the origin of the coordinate system to be 2.6cm to the left of the first wire. (Which is fine, but at the end of the question, you will need to remember to convert this back to the coordinate system which the question uses, where x is in the middle of the two wires).

 

[nerdy_hottie]

So what you're saying is that I've got all my concepts right, just the equations are wrong?

I think I've realized my mistake, and now I have 0=μI1/2∏(x) + μI2/2∏(x+0.052)
I then get 6.8x=2x+0.104
and x is now 0.0217, and to get the final answer I add it to 0.026m and make it negative and I get -0.0477m.

 

[BruceW]

Actually I thought your equation was right, but now I realize it was not right. Your equation in your most recent post is right though. And I think you've got the right answer as well. It might have been easier to use the coordinate system given by the question, but you have successfully got the answer, so all's well that ends well.

 

[asteriatic]

Could you explain this?

Your solution is almost correct. The only mistake is in the sign of the x-values. Since the current in wire 1 is going out of the page, the x-value for wire 1 should be positive, and since the current in wire 2 is going into the page, the x-value for wire 2 should be negative. So your equation should be:

0=μoI1/2∏(x-0.026m) + μoI2/2∏(x+0.052m)

Solving for x using this equation, we get x=0.0412m, which is the distance from the origin to the point where the magnetic field is zero. This makes sense intuitively, as this point is equidistant from both wires and the magnetic fields from each wire cancel each other out at this point.