# Magnetic field between 2 parallel wires

1. Nov 9, 2012

### dawn_pingpong

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution

2. Nov 9, 2012

### 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?

3. Nov 9, 2012

### 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 [Broken]

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!

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4. Nov 9, 2012

### haruspex

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

5. Nov 9, 2012

### dawn_pingpong

Thank yu very much! Now I get it:D