mutual capacitance?

By bi-polar, you probably mean a point where the field begins and ends. Electric circuits have such a point. If the total charge density is zero, the the electric field has to be bipolar. Electric field lines begin at a positive charge and end at a negative charge. In an electric circuit, both electric and magnetic fields are "bi-polar". The reason that a circuit is called a circuit is because the current moves in a closed path. By the generalized Ohms law with complex impedance, the electric field in the circuit also has to define the same closed path. There is an effective electromotive source where the electric field begins and ends. This effective electromotive source is an effective "bi-pole".

The Thevenin Equivalent circuit can be converted to Norton Equivalent. Theorems in that area seem related to the original question. Those theorems do not require inductors to have a dual, but voltage sources become current sources.

For a plate capacitor C = S/d and is proportional to surface.

It is a math joke. E is proportional to the charge density.

The self capacitance of a sphere has the two members: proportional to r and proportional to r squared. S*

Lets get back to reality, shall we? The whole concept of the "capacitance" of an isolated sphere is bogus! Please. Just HOW does one connect their voltage source to "infinity"? Just HOW big is that "infinite" outer sphere? Well, actually it can be ANY size so long as it's big enough! So in reality what we are saying is that IF we have two concentric spheres and we measure the capacitance between them, so long as the outer sphere is much larger than the inner sphere the capacitance of the PAIR depends ONLY on the radius of the smaller inner sphere.

There. Isn't that better now?

Whenever someone uses the word "infinity" they are no longer talking physics. They are talking mathematics.

(snip)

The capacitance for concentric spheres has two terms.

In the limit as the spacing goes to zero, the R squared term is left, as you would expect. (Parallel plate capacitor with spacing delta R and area 4 pi R squared.)

In the limit as the outer sphere goes to infinity, the R term is left.

You can also do it integrating E squared over all space.

-- glen

don't see how "capacitance to infinity" is not the sum of capacitances with all other plates in Universe.

The mutual capacitance matrix that relates charge too potential, as I indicated earlier, is described well in Smythe's book. It is not at all clear to me the self and mutual capacitance described in this way is the dual equivalent of what you get from a circuit dual of self and mutual inductance. It may be, but I have not worked it out. I may not get to it for a while.

I do not know of a common circuit in which self capacitance is an important feature. The closest concept would be that of stray capacitance. But even there, the capacitance arises mostly from capacitance to ground rather than to infinity.

There is no such thing as a line of force. Faraday used lines of force as a convenience. Smart as he was, he did not understand the mathematics of fields. It took Maxwell to understand that aspect. The true law is div B = 0. From that show me that lines of force are closed.

I might as well get in on this band wagon.

The reason a SHORT is called a SHORT is because it takes a short cut to common..

THere.!

Jamie

That's similar to what I have in mind, but not quite -

I don't get this one - self capacitance? Capacitance requires 2 surfaces, plus dielectric, unless things have changed -

-- Rich

Now you're getting warm...

-- Rich

Finally, someone gets it.

A 2-port is what you're describing, which models a transformer (or mutual inductance, generally). Why don't we see the capacitive form in circuit theory, or practice? It's the dual of a transformer, yes/no? Electric flux linkage, vs. magnetic flux linkage?

Can't picture this one -

-- Rich

Yes. The network duality theorem. Crack your old textbook.

Incorrect.

-- Rich

Interesting. That sounds about what I'm looking for, describing the network in matrix form. It seems to imply a capacitive transformer.

But it must be fairly obscure, as I've never seen this formulation. And I don't follow the 'image' thing.

-- Rich

Why couldn't it exist? Interleave plates and dielectric to link electric flux, analogous to magnetically coupled coils.

That's really the thrust of the question.

Well, if the universe is really a big quantum computer, then all we need is information theory and Schrodinger's wave function of 'potentiality', and no need for terra firma -

-- Rich

(snip)

How about the van de Graaf generator? Doesn't seem so far off.

-- glen

(snip)

Usual, but not required. A capacitor stores energy in the electric field, which you can do with a single electrode, usually spherical.

Q=CV, or C=V/Q. If you charge a sphere, its voltage change.

If you don't like that, consider the energy in the electric field around a sphere as a function of the charge on the sphere. Integrate the energy over all space, and compare to C*V*V/2 = Q*Q/C/2.

Next, you can figure out the inductance per unit length for a long straight wire.

-- glen

(snip)

Maybe you do in microwave electronics, though it is harder to say. Inductance and capacitance are harder to separate.

Practical 60Hz inductors are much easier to make into transformers than practical 60Hz capacitors.

Note that inductors are commonly used for fluorescent lamp ballasts at 60Hz, which capacitors are usually used at 20kHz. (The usual electronic ballast.)

-- glen

Capacitance is simply defined as the constant of proportionality between charge and voltage.

C = Q/V

Best,

Fred Diether