# Inductive and Capacitive Coupling Range

#### k1ng 1337

Joined Sep 11, 2020
986
Hi,

What is the maximum distance two parallel conductors will share mutual inductance and mutual capacitance in free space?

I'm looking for clarification so equations would be nice! Fell free to include other elements in the scenario like a voltage source if it makes things more realistic.

Stay cool, we are melting here in Canada

#### Papabravo

Joined Feb 24, 2006
21,259
I'm not sure what is driving this question, but maybe you could opine on why you think there should be a maximum distance. We know that there is a profound difference between lumped parameter models and distributed parameter models. Is that perhaps what you are driving at?

#### k1ng 1337

Joined Sep 11, 2020
986
I'm not sure what is driving this question, but maybe you could opine on why you think there should be a maximum distance. We know that there is a profound difference between lumped parameter models and distributed parameter models. Is that perhaps what you are driving at?
Given the equation F = G(m1m2) / R^2 where range is said to be infinite, I was wondering if there are similar equations for inductance and capacitance between parallel conductors. C = ε(A/d) implies this range to be infinite as well asymptotically approaching zero. I'm trying to understand if there is more to it than these basic equations.

#### Papabravo

Joined Feb 24, 2006
21,259
Given the equation F = G(m1m2) / R^2 where range is said to be infinite, I was wondering if there are similar equations for inductance and capacitance between parallel conductors. C = ε(A/d) implies this range to be infinite as well asymptotically approaching zero. I'm trying to understand if there is more to it than these basic equations.
No, I don't think so.
With particles of opposite charge Coulombs law has a similar form:
$$F\;=\;k_e\cfrac{q_1\cdot q_2}{r^2}$$
Where ke is the Coulomb constant and q1 and q2 are the charges on the particles. As you might suspect the attractive force between particles goes asymptotically to 0 at infinite distance. Since the charges have a sign associated with them, for like charges the forces go to infinity as the distance goes to zero. That is classical physics, and as we all know things get complicated at small distances because quantum mechanics takes over.
In addition we have the strong nuclear force which only operates at very small distance and the weak nuclear force which operates at small distances as well.

Back to inductance and capacitance. There is not much of a problem imagining the capacitance between two plates at large distances being small. Making very long wires and keeping them at a fixed separation is more problematical. If we consider a loop made from parallel conductors the inductance should be a linear function of the length:

https://en.wikipedia.org/wiki/Inductance
There is no implicit limit on length.

#### crutschow

Joined Mar 14, 2008
34,682
There is no inherent limit.

#### MisterBill2

Joined Jan 23, 2018
18,964
There is no inherent limit.
There is no limit to the theoretical coupling, but in the real world the point where the amount of coupling is meaningful and measurable is easily reached. To translate that statement, "As the separation distance increases a point is reached where it does not matter."