Induced current & force between 2 wires

[PsiStar]

These are 2 straight wires parallel for 3 inches. Specifically a 6AWG and 12AWG separated approximately 2 inches. A surge current enters on the 6AWG which has a rising edge of 2500A/us.

This is for a surge device ... I have been working in plain old RF for too long to be certain that I using the math correctly.

 

[Philip Wood]

Presumably - though you don't say - you're trying to find the induced emf in the 12AWG wire? We can help you here, though the induced current and the forces between the wires will depend on the resistance in the circuit containing the 12 AWG wire.

 

[PsiStar]

You are correct Philip ... the induced emf. The loads, wire gauge, & length vary for other similar projects. This criteria is the immediate.

This type of problem is recurring for me. My approach in the past probably produces correct results but is gross overkill. Time for review of the physics.

 

[Philip Wood]

Psistar: The thumbnail I append derives the emf in a rectangular loop, in terms of quantities you've given above - except the distance I've denoted as b. You need to supply a value for this. A long straight wire and a rectangular loop is perhaps not quite the set-up you envisaged, but it's one where the maths is do-able! If you also know the resistance of the loop you can find the current in it, and then you can find the force between the loop and the wire, as a function of time.

 

[PsiStar]

Thank you for that very straight forward explanation and math.

A question about your diagram, what is quantity "b". It looks like it is the distance from the 6AWG wire to the far side of the loop.

 

[Philip Wood]

That's exactly what it is. Good luck!

 

[PsiStar]

The far side of the loop is quite undefined. Is a loop necessary or is this just one method of analysis?

 

[Philip Wood]

What do you mean by 'undefined'? It's whatever distance you choose to make it! Use the formula to guide your choice. I think that a loop of some sort is inevitable, as presumably you want the 12AWG wire to be part of a circuit, even if the circuit is completed only by a voltmeter, to measure the induced emf. As I explained, I chose a rectangular loop because it's easy to calculate the induced emf. Most other cases are very difficult. And another advantage is that you can have a rectangular coil of n turns, which will give n times the emf in a single loop.

 

[PsiStar]

These circuits are in railroad shelters. Sometimes a man-sized metal box, sometimes a metal hut that can hold a few men, sometimes a wooden structure.

Here is what is confusing me. I "want" to relate the induce EMF to the length of the wires parallel in some specified close proximity to each other as being the significant factors (length & distance). But the "b" dimension logrithmically directly relates this dimension to the far side of the loop. The further away that far side, the greater the induced EMF.

 

[Philip Wood]

Ah: the wires are already there, and you want to find the emf that a varying current in one induces in the other? I Googled "mutual inductance of parallel wires" and there were formulae offered on several sites.

 

[PsiStar]

Really? I know google, bing, & even baidu but feel ... lacking. What did you find that you think fills the bill?