# Two wires, where is magentic field zero?

• FuzzyDunlop
In summary, the question asks where on the y-axis the magnetic field is zero when two wires carrying currents of 53 A and 37 A are placed in opposite directions parallel to the x-axis at y-coordinates 3 cm and 13 cm. The equation B(r)=Iu/[2(pi)r] is used to solve for the position r where the magnetic fields of the two wires are equal. The final equation is [(10-r)*53]/r=37, which gives a solution of r=5.88 cm. Adding the initial position of y=3 cm, the final answer is y=8.88 cm.
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

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.

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

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.

## What is a magnetic field?

A magnetic field is a force field that surrounds a magnet or electric current and exerts a force on other magnets or moving electric charges.

## How does the magnetic field affect two wires?

The magnetic field affects the two wires by exerting a force on the moving electric charges within the wires. This force can cause the wires to attract or repel each other depending on the direction of the current flow.

## Where is the magnetic field zero between two wires?

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

## What factors can affect the location of the zero magnetic field point?

The location of the zero magnetic field point can be affected by the distance between the two wires, the strength of the current flowing through the wires, and the orientation of the wires relative to each other.

## How can the zero magnetic field point be determined experimentally?

The zero magnetic field point can be determined by using a compass to map out the magnetic field around the two wires. The point where the compass needle does not deflect is the zero magnetic field point.

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