Magnetic field between 2 parallel wires

[dawn_pingpong]

Homework Statement

Sorry. I know this question is on the forum somewhere, but I still don't get it... Thus.

For parallel wires, at the mid-point of the wires, what is the strength of the magnetic field? Do I use the formula $B=\frac{μi_{1}i_{2}L}{2∏r}$, or is it the sum of
$B=\frac{μi}{2∏r}$, for both wires? I'm really confused:(

For example,
Two parralel wires are 8 cm apart. The magnetic field halfway between them is 300 uT. What equal currents must be in the wires?

I would use equation no. 1, but it is actually 2x equation (2). Thus I don't really get, how to calculate the magnetic field between 2 parallel current carrying wires? And when to use equation (1)?

Thank you.

Homework Equations

The Attempt at a Solution

 

[haruspex]

For one wire you would obviously use eqn 2. For two wires it will be just the sum of the fields due to each wire, so just use eqn 2 for each and add them up. (Note that the currents must be in opposite directions or the fields would cancel.)
I don't recognise eqn 1. It doesn't make sense dimensionally. Where did you find it?

 

[dawn_pingpong]

Oh, okay, thanks!

Uh the 2nd formula is in quite a lot of places actually, though I might have misunderstood it... Places like http://www.cartage.org.lb/en/themes/sciences/physics/electromagnetism/Magnetostatics/MagneticField/Forcesoncurrents/parallelwires/parallelwires.htm

and the attached is the Halliday Textbook... In such a case, what do they mean by the 1st equation? Is it the force acting on one wire or something? Thanks!

 

[haruspex]

what do they mean by the 1st equation? Is it the force acting on one wire or something?

Yes, it's the force the wires experience from each other, not the field.
Field at 1st wire = B₁ = μ i₂/d
Current in 1st wire = i₁
Force per unit length acting on first wire = B₁ i₁ = μ i₁i₂/d
Force on 1st wire of length L = μ i₁i₂L/d

 

[dawn_pingpong]

Thank yu very much! Now I get it:D