# Capacitance of current carrying wires (Transmission Line)

Let me explain my primitive understanding of a capacitor.

In electrostatics, a conductor containing accumulated charges attracts opposite charges in a conductor that's separated by an insulator, this setup is called a capacitor.

While studying transmission lines, we associate a capacitance between the two lines or line and ground etc. But how is this possible, don't we need charges to accumulate to attract charges on the other conductor or ground? If the transmission lines are carrying current how do charges accumulate? The root of the question seems to be "Do current-carrying wires produce an electric field outside in addition to the magnetic fields?" If the answer is yes, then this electric field might attract the opposite charge in the other conductor, but I'm not sure.

Edit

well, you're studying transmission lines, so you definitely know Maxwell, and you also know that electrostatics is not a model you can model the transmission line with.

In the book I'm reading currently Stevenson and Grainger, the expression for capacitance between two lines in a single phase 2 wire system is found just like finding the capacitance between two oppositely charged straight long conductors placed in parallel. I'm not able to understand why this is possible, is there no need to account for the current at all?

I found a gif on wiki, Is this the answer? The bunching up of electrons causes a capacitance?

• well, you're studying transmission lines, so you definitely know Maxwell, and you also know that electrostatics is not a model you can model the transmission line with. Aug 28, 2021 at 10:38
• @MarcusMüller I don't know how to think about it, can you please explain Aug 28, 2021 at 11:22
• I can't explain Maxwell's equations in a comment. this is literally a full semester of Maxwell and wave theory that you study at university. Aug 28, 2021 at 12:17
• @MarcusMüller I've added an edit, can you please check, I just want to know how that's possible Aug 28, 2021 at 12:18
• @MarcusMüller I'm not really that dumb, I can understand you can't explain EM theory in a comment. I'm just asking for directions to comprehend what's happening :| Aug 28, 2021 at 12:22

In electrostatics, a conductor containing accumulated charges attracts opposite charges in a conductor that's separated by an insulator, this setup is called a capacitor.

Not really! What you mention is a special type of configuration of capacitor for storing electrical energy in electric field.

Anything that can store electrical energy in form of electric field can be considered as capacitor. That is why even a single conductor can be considered as a capacitor (because it also has some self capacitance).

But how is this possible, don't we need charges to accumulate to attract charges on the other conductor or ground?

Another way to store electrical energy between conductors is to connect both conductors by a battery /alternator(different terminals) which causes a potential difference between the conductors and then charges start accumulating on both conductors and setup an electric field.

"Do current-carrying wires produce an electric field outside in addition to the magnetic fields

If there is a potential difference between wires then of course they produce electric field outside.

Note: even a single conductor with some charges produce normal component of electric field outside of conductor, which we generally modelled as self capacitance of conductor , and this effect can be seen in conductor carrying current which causes surface charges (sometimes) to appear and hence electric field outside. (But this effect we generally don't consider because of small value of self capacitance).

If the answer is yes, then this electric field might attract the opposite charge in the other conductor,

Of course it try to attract depending on how much charges are there or what force they apply and what is orientation of all wires (whether net forces cancel each other or not).

• Thank you for answering. When we have two wires connected to an AC source, do charges in one conductor flow along the side facing the other conductor? I also don't understand what self capacitance is, can you please explain? Aug 28, 2021 at 11:46
• @Aravindh Vasu 1.if assume air as perfect insulator then charges do not flow from one conductor to another, but mind you for current to establish we don't need charge to flow always even a varying electric field is enough for it which we also called as displacement current. Aug 28, 2021 at 12:00
• 2.if any conductor connected to a battery acquire some surface charges , then these surface charges create its own electric field outside the conductor, and hence we can say there is some electrical energy stored from conductor to infinity , and this can be assumed as self capacitance of the conductor. Aug 28, 2021 at 12:04
• I've added an edit, can you please address that if possible? Aug 28, 2021 at 12:32
• @Aravindh Vasu , can you precisely point out, which part of your question, I didn't answer? Because in your edit I don't see any changes apart from quoting a comment. Aug 28, 2021 at 13:56