Two wires, where is magentic field zero?

[FuzzyDunlop]

Homework Statement

Two wires carry current I1 = 53 A and I2 = 37 A in the opposite directions parallel to the x-axis at y1 = 3 cm and y2 = 13 cm. Where on the y-axis (in cm) is the magnetic field zero?

I1= 53 A
I2=37A

Homework Equations

B(r)=Iu/[2(pi)r]

The Attempt at a Solution

I thought i could solve this guy by setting the strengths of the fields equal to each other and finding r. Much of it would cancel out so I basically had

53u/(2[pi]r)=37u/(2[pi](10-r)

[(10-r)*53]/r=37

r=5.88

and then I added 3 to r since the starting position is y=3. It made sense to me but obviously i messed up somewhere.

 

[LowlyPion]

If the current in the wires is going in opposite directions what do the field vectors do in the distance between the 2 wires?

 

[nlightner]

I would first commend the student for attempting to solve the problem and using the appropriate equation for magnetic field. However, there is a mistake in the calculation of r. The correct approach would be to set the magnetic field equations for the two wires equal to each other and solve for r. This would give a value of r= 5 cm, which is the distance from the wire at y1 where the magnetic field is zero. The mistake in the student's calculation was that they used 10-r instead of r in the denominator of the second equation. It is important to pay attention to the direction of the current and the distances in the problem to avoid such mistakes. Overall, the student showed good understanding of the concept of magnetic fields and their calculation.