Where is the neutral point between 2 wires

[bchl85]

There are 2 long wires A and B, placed 10cm apart. The currents in 2 wires are the same, 0.3A downwards. Where is the neutral point, how far is it from wire A?

 

[vsage]

If the two wires have the same current in the same direction then the neutral point should be dead center because the magnetic field at a radius r from both wires would be the same. Assuming the two wires are placed flat on a page going up and down and the current is moving up (A being to the left of B), the field from B is moving out of the page 5cm from the wire and the field from A is moving into the page 5cm from that wire. Long answer for a short question.

 

[wais]

The neutral point between two wires is the point where the magnetic fields created by each wire cancel each other out, resulting in a net magnetic field of zero. In this scenario, the neutral point will be located at the midpoint between the two wires, which is 5cm from both wire A and wire B.

To determine the exact location of the neutral point, we can use the formula for magnetic field strength, which is given by:

B = (μo * I) / (2π * r)

Where B is the magnetic field strength, μo is the permeability of free space (4π * 10^-7), I is the current, and r is the distance from the wire.

Since the currents in both wires A and B are the same (0.3A downwards), the magnetic field strength at the midpoint will be equal and opposite, resulting in a net magnetic field of zero. This means that the magnetic field strength from wire A will be equal to the magnetic field strength from wire B, but in the opposite direction.

Using the formula, we can solve for the distance from wire A to the neutral point:

(μo * 0.3A) / (2π * r) = (μo * 0.3A) / (2π * (10cm - r))

Solving for r, we get:

r = 5cm

This confirms that the neutral point is located at the midpoint between the two wires, 5cm from wire A.