acconductorsparallel
If we have one conductor through which current flows, and we place second conductor near it, the conductor with current flowing will induce electron flow in the second conductor.
Can we detect the (parasitic) power loss in the first conductor which induces the electron flow in the conductor near it? If yes, how?
For an inductor, how does the electron flow (current) lag behind the supply voltage?
In an inductor which has no magnetic field already established, the application of electricity initially sees an open circuit (little current flow.) As the magnetic field builds, the current also builds, and it eventually behaves like a solid conductor (full current flow.) So the current lags the supply voltage due to the delay in establishing the magnetic field.
(If you then instantly disconnect the inductor, the magnetic field will collapse in reverse as quickly as it can. With no resistance to slow it down, dv/dt dictates that the voltage will go exponentially high. This is called "inductive kickback" and can be problematic, even dangerous.)
For a capacitor, how does the electron flow (current) lead the voltage?
In a discharged capacitor, the potential (electric field) between the two plates is nothing, so no current flows. Application of any electricity initially sees a short circuit (full current flow.) As the plates start charging up, the current decreases, and eventually behaves like an open circuit (little current flow.) So the current leads the supply voltage due to the delay in establishing the electric field.
(If you then instantly disconnect the capacitor, the electric field remains static, like static electricity. It may remain there for years, ready to zap you, such as in older televisions and radios.)
The key similarity between the two is that it takes time for magnetic fields to build/collapse and plates to charge/discharge; this delay creates an imbalance between the voltage and current measured at each device... and we call the ratio of this "Power Factor."
The above is the formula for the inductance of parallel wires where s is distance between wires, L is the overall length and d is wire diameter and here is a calculator that uses the formula.
For series resistance you will find many references on google for this and please note that it is ambient temperature dependant. There are plenty of references for skin effect also but not so many for the formula for proximity effect but hopefully this reference from wiki might prove useful.
Finally, once you have the resistance, inductance and capacitance you can use the standard formula for characteristic impedance (applies to any length of wire of course and is still valid down to DC): -
You haven't considered "G" but this is usually a very large resistance and its effect is negligible.
So now you have the impedance looking into an infitely long line of cable. However, you want the impedance looking into 100 metres of such cable so you will then have to work with reflection coefficients and the load impedance (stated as unloaded in the question) BUT YOU CANNOT ignore these load effects (and reflections) if you want a proper answer.
Reflections will occur with any incorrectly terminated cable: -
And these can effect results significantly even at moderate frequencies like 100 kHz. At 100 kHz the wavelength is 3 km but this is probably going to be more like 2 km. Major things happen at a quarter of this wavelength i.e. an open circuit can look like a short circuit and a short circuit can look like an open circuit so 500 metres is still pretty close for creating major errors when considering a cable that is 100 metres long.
Best Answer
No, current in the first wire does not induce current in the second. It's the derivative of the current that induces a voltage (open circuit) or current (shorted) in the second.
In the cases where there is power transfer (the second wire not open, for example), you can detect the loss of this power in driving the first wire.
What you are describing is a transformer, just that it has a unusual geometry and the coupling isn't very good. Just like with any transformer, power coming out the secondary came from power put into the primary. With the right circuit, the power being put into the primary can be measured, and thereby varying power being drawn from the secondary can be measured.
Keep in mind that when the secondary is open circuit, it's basically not there from the view of the primary. The transformer then degenerates to just a inductor.