# Significance of magnetic flux between wires

• Faiq
In summary, the total magnetic flux density due to the current in two wires that are laid side by side and carry equal currents in opposite directions is negligible because the magnetic fields created by each wire cancel each other out when measured at a distance between the wires. This cancellation is only true at a certain distance and can vary if the wires are spaced farther apart or if the current is very high.
Faiq

## Homework Statement

Two wires are laid side by side and carry equal currents in opposite directions. Explain why the total magnetic flux density due to the current in the wires is negligible

2. The attempt at a solution
I know that having a different direction for the current results in opposable magnetic fields. What I don't understand is how does opposable magnetic fields results in their cancellation. The magnetic field due to both wires in between them will always be in the same direction. So how do the magnetic fields cancel out?

The wires are laid side by side implies that they are pretty close together, perhaps just separated by a layer of insulation. I figure they want you to comment on the field at some distance from the pair, not necessarily between them.

Ohhhhh thanks got it. But if we take into account the middle portion, the magnetic field there is 2 times the usual right?

Faiq said:
Ohhhhh thanks got it. But if we take into account the middle portion, the magnetic field there is 2 times the usual right?
Well, that depends upon what you define to be "the usual" and where precisely between the wires you measure it

By between I mean the magnetic flux in extreme middle of both wires and by usual I mean, the magnetic field created my one of the wire at the same distance

Faiq said:
By between I mean the magnetic flux in extreme middle of both wires and by usual I mean, the magnetic field created my one of the wire at the same distance
Then I would agree with your assessment that the field strength is doubled at that locus.

oh okay thanks

Apologies for disturbing you again but I have one question
If the current in both wires is very high and the distance between both wires is also high, will the magnetic field at some point still be negligible?

Faiq said:
Apologies for disturbing you again but I have one question
If the current in both wires is very high and the distance between both wires is also high, will the magnetic field at some point still be negligible?
It's a matter of scale. You can always make any finite distance between the wires insignificant by backing off far enough; Infinity gives one a lot of room to maneuver

Oh okay

## 1. What is magnetic flux?

Magnetic flux is the measure of the total magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of Weber (Wb).

## 2. How does magnetic flux affect wires?

The magnetic flux between wires is a result of the interaction between the magnetic fields produced by the wires. When the wires are placed close to each other, the magnetic fields interact and can either attract or repel each other, depending on the direction of the current flowing through the wires.

## 3. What is the significance of magnetic flux between wires?

The significance of magnetic flux between wires lies in its ability to influence the behavior of electric currents. When the wires are in close proximity, the magnetic flux between them can cause the currents to either increase or decrease in strength, depending on the direction of the current and the orientation of the wires.

## 4. How is the magnetic flux between wires calculated?

The magnetic flux between wires can be calculated using the formula Φ = B x A x cosθ, where B is the magnetic field strength, A is the area of the wire, and θ is the angle between the wire and the magnetic field. This formula is known as the flux density formula.

## 5. What factors can affect the magnetic flux between wires?

The magnetic flux between wires can be affected by the distance between the wires, the strength of the current flowing through the wires, and the orientation of the wires in relation to each other. Other factors such as the material of the wires and the presence of other magnetic fields can also impact the magnetic flux between wires.

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