# every conductor has inherent capacitance

Discussion in 'Homework Help' started by PG1995, Oct 29, 2011.

1. ### PG1995 Thread Starter Active Member

Apr 15, 2011
753
5
Hi

A capacitor has capacitance due to different types of charge of its plates. Okay. This is understandable. A conductor is said to have uniform spread of charge and charges (i.e. electrons) can flow one place to another to neutralize an imbalance of charges. Still, it is said every conductor has an inherent capacitance. How is this possible? In case of a capacitor energy is invested to create an imbalance of charge; there is nothing 'natural' in this case. How can a conducting wire have any capacitance? Please help me with it. Thank you.

Regards
PG

2. ### crutschow Expert

Mar 14, 2008
12,552
3,076
Typically the capacitance is between the wire and some nearby ground or another wire which provides the other "plate". Obviously the capacitance is small, but can have an effect in high frequency circuits. For example a CAT5 twisted-pair of conductors has a capacitance of about 52pf/meter.

PG1995 likes this.
3. ### PG1995 Thread Starter Active Member

Apr 15, 2011
753
5
Thank you, Carl.

Okay. Now I understand that capacitance can exist between a conductor and some nearby object such as wire or ground. But still to have some capacitance one of the 'plates' should have uneven spread of the charge so that it can disturb the charge distribution in a nearby object. Say, the conducting wire has an evenly spread charge throughout it, then how can it affect anything nearby to develop capacitance when it is a neutral conducting material.

I have also read that capacitance can exist between different sections of a same wire. For example, please have a look on the linked scan: http://img11.imageshack.us/img11/8789/inductrcapacitance.jpg

Please keep your explanation simple and don't make things more complicated. Thanks a lot.

Regards
PG

Dec 26, 2010
2,147
298
It's not as simple as that: in fact it's a bit counter-intuitive. Any conducting object has capacitance, even if it is completely isolated from other bodies and distant from them.

Think of the sphere of a Van de Graff generator. This stores charge, and energy, (as you may find out to your considerable cost if you get too close!). The charge locates to the exterior of the dome, even if there may be no nearby grounded object, except the "cold" end of the generator, and of course the Earth itself.

It goes beyond that that. Even a body floating in space, if it acquires charge will develop a predictable potential and will radiate an electric field. The capacitance of a theoretical body infinitely separated from other matter can be calculated.

http://en.wikipedia.org/wiki/Capacitance#Capacitance_of_simple_systems

Last edited: Oct 30, 2011
5. ### steveb Senior Member

Jul 3, 2008
2,433
469
This isn't quite correct. A capacitor has capacitance due to it's geometry, not due to the different types of charge on its plates.

This is also not quite correct. A conductor does not necessarily have a UNIFORM spread of charge. You are correct that the charges can flow, but they do not flow to neutralize an imbalance of charge. They flow and move to positions that neutralize the electric field within the conductor.

OK, so here it is better to think of every conductor having its own capacitance. Hence, there is capacitance with one conductor, two conductors or any number of conductors. The capacitance then becomes a matrix with many components. One conductor has one component, two conductors have 4 components, three have nine ... and so on. The case of two conductors (with 4 capacitive components) can be simplified to one component if we only care about the voltage difference between the two plates and we assume that the charges on the plates are equal and opposite.

So, when we talk about capacitance of one conductor versus two conductors, we are really talking about two different (although closely related) quantities.

Looking through all my electromagnetics books, I find that the treatment given by Melvin Schwartz in his "Principles of Electromagnetics" is the best. He considers the general treatment of capacitance for any number of conductors and shows how the principle of superposition can be used to derive the concept of a capacitance matrix which depends only on the system geometry (not the charge or voltage itself).

I know you are looking for a simple explanation, and this is perhaps beyond what you want. However, the concepts given are not really that complex and sometimes you have to "bite the bullet" and really dive into the details to make better progress.