I would like to have a rough estimate of the capacitance per unit length of a system composed by N parallel identical straight wires. I tried to sketch the capacitance network but I'm able to solve it only up to 4 wires... Any idea how to smplify the problem?
It has been a loong time since I did basic electricity and fields.
The electric field starts at potential V and, with a constant dielectric, will linear with distance go to 0V (Gnd). This means that in the middle you find a potential of V/2.
If we place a very thin electric plate at 1/3d from V, the potential of the plate will then be 2/3V:
If you would externally set a potential of 2/3 V on that plate the electric field, and thus the capacitance would be the same.
This means that all your wires in the middle do not make a difference and can be ignored.
But to solve the capacitance network you don't really need to know all these details right?
As you can see, the voltage on those line places a crucial role.