# The distance where the magnetic field of two wires is zero

• DottZakapa
In summary, the distance from the wire carrying current i at which the magnetic field is zero is d/4, using the Biot-Savart equation and setting up a proportion between the distances of the point from each wire.
DottZakapa
Homework Statement
The distance between two parallel long wires, carrying currents equal to i and 3i respectively, is d as shown in the picture. What is the distance from the wire carrying the current i at which the magnetic field is zero
Relevant Equations
guess biot-savarat
Homework Statement: The distance between two parallel long wires, carrying currents equal to i and 3i respectively, is d as shown in the picture. What is the distance from the wire carrying the current i at which the magnetic field is zero
Homework Equations: guess biot-savarat

Being two long straight wires i can apply Biot-Savart equation. The currents are flowing in the same direction, hence at some point in between the sum of the two magnetic fields cancels.
My attempt
μ0i/(2πd)=μ03i/(2πd1)
and solve for d.
But does not leads to the correct solution. can't spot the mistake.

There is some confusion in your post regarding the use of symbol d. It is used to indicate the unknown distance and also the known distance d between the two wires.

Lets call x the distance from wire carrying current i of point P where the magnetic field is zero . Then the distance of point P from the other wire is d-x. What equation can you make using those distances?

DottZakapa
don't know why i couldn't find a way to express it...now i got it.
i/x=3i/(d-x) ... ⇒ x=d/4
Thank you, very kind

Delta2

## 1. What is the distance where the magnetic field of two wires is zero?

The distance where the magnetic field of two wires is zero is called the neutral point. It is the point between the two wires where the magnetic fields of the two wires cancel each other out, resulting in a net magnetic field of zero.

## 2. How is the neutral point calculated?

The neutral point can be calculated using the equation: d = (μ0 * I1 * I2)/(2π * r), where d is the distance between the two wires, μ0 is the permeability of free space, I1 and I2 are the currents in the two wires, and r is the radius of the wires.

## 3. Can the neutral point be changed?

Yes, the neutral point can be changed by altering the distance between the two wires, the currents in the wires, or the radius of the wires. However, the neutral point will always exist at a certain distance between the two wires.

## 4. What is the significance of the neutral point?

The neutral point is important in understanding and predicting the behavior of magnetic fields created by two parallel wires. It can also be used in various applications, such as in designing magnetic shields to protect sensitive equipment from external magnetic fields.

## 5. How does the neutral point affect the strength of the magnetic field?

The neutral point does not change the strength of the magnetic field, but it changes the direction of the magnetic field. At the neutral point, the magnetic field is cancelled out and becomes zero. As you move away from the neutral point, the magnetic field strength increases in one direction and decreases in the opposite direction.

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