Significance of magnetic flux between wires

[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?

 

[gneill]

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.

 

[Faiq]

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

 

[gneill]

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

 

[Faiq]

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

 

[gneill]

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.

 

[Faiq]

oh okay thanks

 

[Faiq]

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?

 

[gneill]

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

 

[Faiq]

Oh okay