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

In summary, two parallel conducting wires are placed along the z axis, with Wire 1 crossing the x-axis at x = -2.60 cm and carrying a current of 2.00 A out of the xy-plane, and Wire 2 crossing the x-axis at x = 2.60 cm and carrying a current of 6.80 A into the xy-plane. The magnetic field is zero at x = -0.0477 m.
  • #1
nerdy_hottie
19
0

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=μoI/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=μoI1/2∏(x+0.026m) + μoI2/2∏(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.
 

Attachments

  • capa6.jpg
    capa6.jpg
    3.8 KB · Views: 643
Physics news on Phys.org
  • #2
nerdy_hottie said:
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).
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 

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

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can act on a magnetic object or a moving electric charge. It is represented by lines of force that indicate the direction and strength of the magnetic field.

2. How is a magnetic field created?

A magnetic field is created by moving electric charges, such as electrons. In the case of two antiparallel current-carrying wires, the electrons moving in opposite directions create a magnetic field around the wires.

3. What is meant by antiparallel current-carrying wires?

Antiparallel current-carrying wires refer to two wires that are parallel to each other but have opposite directions of current flow. This means that the electrons in one wire are moving in the opposite direction of the electrons in the other wire.

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

The magnetic field is zero at the midpoint between the two wires. This is because the magnetic fields created by the two wires cancel each other out at this point.

5. How does the distance between the wires affect the location of the zero magnetic field?

The location of the zero magnetic field between two antiparallel current-carrying wires depends on the distance between the wires. As the distance increases, the zero field point moves closer to the midpoint between the wires. Vice versa, as the distance decreases, the zero field point moves further away from the midpoint.

Back
Top