What is the current through a second separate wire?

[TekuConcept]

I have two wires, each 1 meter in length. They are at a parallel distances (d) of 5cm from each other.
I send a current through one wire: I₁ = 2 amps, and what I want to find is the current induced on the other wire: I₂ = ?

I can find B with the following formula (given a radius - which I could substitute with d):
B = μ₀I/2πr
For a transformer, I could find I₂ using the following formula:
I_p = I_s(N_s / N_p)​

(Where I_p is the primary current, I_s is the secondary current, N_s is the number of loops for the secondary coil, and N_p the number of loops for the primary coil) However, the transformers I know, all use a core of some sort - which will stretch the magnetic field.

Through my hours of searching, I have come across this formula: ΔF = ΔL(μ₀ I₁ I₂ / 2 π d). I could solve for I₂ but ΔF is still unknown here - I guess I could ask 'How do I find ΔF?,' never the less, perhaps there is yet another formula I'm missing out on?

I would like to know of a formula such as: I = f(B, v) where B is a force from say a permanent magnet, moving at a constant speed of v.

 

[berkeman]

I have two wires, each 1 meter in length. They are at a parallel distances (d) of 5cm from each other.
I send a current through one wire: I₁ = 2 amps, and what I want to find is the current induced on the other wire: I₂ = ?

I can find B with the following formula (given a radius - which I could substitute with d):
B = μ₀I/2πr
For a transformer, I could find I₂ using the following formula:
I_p = I_s(N_s / N_p)​

(Where I_p is the primary current, I_s is the secondary current, N_s is the number of loops for the secondary coil, and N_p the number of loops for the primary coil) However, the transformers I know, all use a core of some sort - which will stretch the magnetic field.

Through my hours of searching, I have come across this formula: ΔF = ΔL(μ₀ I₁ I₂ / 2 π d). I could solve for I₂ but ΔF is still unknown here - I guess I could ask 'How do I find ΔF?,' never the less, perhaps there is yet another formula I'm missing out on?

I would like to know of a formula such as: I = f(B, v) where B is a force from say a permanent magnet, moving at a constant speed of v.

Welcome to the PF.

Your post is a bit confusing. You at first ask about just 2 parallel wires. In that case, there is no induced current in the 2nd wire. But then you ask about current loops, where there would be an induced voltage and current. Can you please describe the geometry in more detail?

 

[TekuConcept]

Visualizations Are In Order

Ah, yes... here are pictures and other references to help demonstrate:

Here is the first picture to help visualize what I described in the beginning (basically if I were to create an electromagnetic coil with a driver nail as the inductor's core):

Here is the second picture demonstrating my main objective (given a magnetic force [ B ], relative speed [m/s], relative distance [d], and time [Δt], find the induced current of the wire ):

As a visual demonstration, here is a YouTube clip on 'Magnetic Induction'


Faraday's Law of Induction may be what I am looking for - using the Maxwell-Faraday equation:
∇ x E = -(∂B / ∂T)
(I am only just starting to re-learn all that goes with ∇ again - ie: gradient, divergence, & curl - so I can't determine if I found my answer just yet)

 

[davenn]

OK so the second wire ISNT the return wire for the first one

that's what we wanted to clarify :)

Dave

 

[sophiecentaur]

Ah, yes... here are pictures and other references to help demonstrate:

Here is the first picture to help visualize what I described in the beginning (basically if I were to create an electromagnetic coil with a driver nail as the inductor's core):

Here is the second picture demonstrating my main objective (given a magnetic force [ B ], relative speed [m/s], relative distance [d], and time [Δt], find the induced current of the wire ):As a visual demonstration, here is a YouTube clip on 'Magnetic Induction'Faraday's Law of Induction may be what I am looking for - using the Maxwell-Faraday equation:
∇ x E = -(∂B / ∂T)
(I am only just starting to re-learn all that goes with ∇ again - ie: gradient, divergence, & curl - so I can't determine if I found my answer just yet)

This is the vital relationship. The magnetic flux, linking the circuit must be changing with time. Stationary or DC won't induce any voltage. Why not just go to Wiki and see what they have to say about electromagnetic induction? (Note the Counterexample in the Wiki page, though)

Be careful about that YouTube video. Electrons are not the slightest bit like the way they're shown. Just stick to 'Current' if you can .

 

[TekuConcept]

Stationary or DC won't induce any voltage. Why not just go to Wiki and see what they have to say about electromagnetic induction? (Note the Counterexample in the Wiki page, though)

Yes, I know stationary and DC sources won't induce any voltage - my design is really a spinning motor-generator (similar to those used in the old Lego Mindstorms), and yes I did read the Wikipedia article: 'electromagnetic induction' before sharing the above images and duly noted the counter examples near the bottom - I reference the Maxewell-Faraday equation because of it's accuracy. (non the less, thank you for your suggestion)

This is the vital relationship. The magnetic flux, linking the circuit must be changing with time.

I haven't yet figured out how curl (∇ x E) works in vector calculus, but are you suggesting I found my answer already?
(just want to confirm - solve for B which includes distance, then solve the partial derivative given change in time, which should yield the curl of the induced current)