CAPACITOR COMPLAINTS

On Wimshurst machines and capacitors:

First charge up a Leyden jar using a Wimshurst Machine (or other source of high voltage.) Now, carefully remove the inner metal from the jar. Now remove the outer metal. Discharge everything, then hand the parts around the classroom. Next, put the parts together again, connect the two metal cylinders, and BANG!, there is a loud discharge.

Doesn't this prove that the energy in a capacitor is stored in the dielectric? No.

Whenever you take apart a Leyden jar or other high voltage capacitor, there is a corona effect which makes very strange things occur. When you electrify a Leyden jar, and then you pull the inner metal cylinder out of the jar, the capacitance value drops, and this makes the potential difference skyrocket to enormous levels. The potential tries to become huge but it cannot, because instead it creates corona along the metal edges, and and it leaks the excess charge into the air. This corona allows the opposite electrical charges to "paint" themselves onto both sides of the dielectric "jar" surface. So, if you pull a leyden jar apart, the sharp edges of the metal plates sweep along and transfer a large percentage of the separated charges from the metal plates to the glass surfaces. The energy is still there! It's still stored as a field in the dielectric, but those separated charges are not on the mental plates anymore. Instead they are now TRAPPED ON THE GLASS SURFACE! Strange idea, huh? A capacitor with no plates, just a dielectric.

Now reassemble the Leyden jar: momentarily touch each metal plate to ground, and put it back together again. You'll find that it's still strongly electrified! The trapped charges on the glass surface can still induce equal charges on the adjacent metal plates. Touch the two terminals with your fingers and BOOM!, the momentary current in your muscles will throw you across the room.

This strange effect leads many people to claim that the energy in a capacitor is permanently trapped in the dielectric, and that it is not stored in the electric field. This is wrong.

In order to properly perform the take-apart capacitor experiment, you must execute the entire demonstration inside a big tank full of oil. This prevents the corona discharges from spewing charges from the edges of the plate onto the dielectric.

Or, perform the whole experiment at 1.0 volts, not at 10,000 volts. (Use an electrometer to measure the voltage.) You'll find that the dielectric doesn't store energy anymore. In order for the charges to spray onto the dielectric, the voltage must be high.

Or, use high voltage but do this instead: before doing anything, take apart the leyden jar. Now, lay the metal parts on a plastic sheet and use a Wimshurst machine to charge them up. Next, use plastic tongs to assemble the leyden jar. (The voltage across the plates will be very low.) NOW perform the leyden jar dissection. It shouldn't work anymore, since the initial voltage is low enough that it will prevent corona discharges from painting any charges on the dielectric.

Capacitors: physicists vs. engineers

 
> For the charge to flow in a circuit, there has to be a closed path.
> Right, sir! Please correct me if I am wrong.

No, there must be a closed path ONLY if the charges must flow continously in the circuit forever (pure DC). But if the charges flow briefly, or if they flow back and forth (AC), then an open path is sometimes acceptable.

For example, with a metal rod 1 meter in length, it is possible to create a standing wave of charges oscillating lengthwise in the rod with frequency 150MHz. Inside the rod, the charges move back and forth (this resembles the motions of the compressible air inside one pipe of a church organ.) The charges within the rod are acting like a compressible fluid.

At far lower frequencies, the electric current can still be large if the ends of an open circuit are joined to the plates of a capacitor. On the metal surfaces between the plates of the capacitor, the quantities of charge carriers behave as a "compressible fluid", while the charges within a wire behave as an "incompressible fluid."

> In the capacitor, the charge flows from one plate to the other. Let's
> assume that air is the dielectric between the 2 plates of the capacitor.
> So, there is no physical conducting path between the 2 plates. So,
> it's like an open circuit. How can we say that the charges move from
> one plate to the other?

Two ideas are necessary:

1. Metals are always full of movable charges even when they are electrically neutral. They contain a "fluid" made of electrons, and a "solid" made of protons (made of the nuclei of metal atoms.)

2. Negative charge can repel the "hidden" negative charges within a nearby neutral piece of metal.

If you forcibly inject electrons into one plate of a capacitor, these electrons will repel the electrons hidden within the other uncharged plate, and these other electrons will be forced out of the capacitor's other terminal. However, if the other capacitor terminal is connected to nothing, then those electrons cannot leave the other plate. They will continue to repel the electrons in the first plate, and for this reason very few electrons can be forced into the first plate. The rule for most capacitors is: the current in both capacitor terminals is always the same. This means: if charge is injected into one capacitor plate, then an equal amount of charge is pushed out of the other capacitor plate, and if equal charge cannot leave the second plate, then we CANNOT force charge into the first plate.

If we ignore the space between the plates, the capacitor SEEMS to be a kind of conductor. However, it is a strange "conductor" where the two terminals are connected by electrical forces which reach across a narrow space. It is not a true conductor, but neither is it a simple insulator.

> Sir, I have asked the same to my undergraduate professors, but they find
> it too trivial to answer. Thus, I have never been able to understand
> this concept. 

I think this concept is explained very badly in physics textbooks. In physics, a single metal sphere is considered to be a "capacitor," and two metal spheres with a large separation between them is also a "capacitor." Yet conceptually these are very different from capacitors used in electric circuits.

In both these situations, the flow of charge into one sphere NEED NOT BE EQUAL to flows of charge in the other sphere or elsewhere. The entire universe serves as an extra unseen capacitor plate. Yet in electronics, "capacitor" means only one thing: "two closely-spaced plates." As far as electronic equipment is concerned, capacitors only have two plates, and the current in one terminal must always equal the current in the other terminal. This is not true for two distant conductors, but this "general case" in textbooks is MUCH harder to understand. Physics textbooks examine the general case where the currents in the capacitor terminals are not equal, and the electrostatic coupling between the plates is not very strong. Conventional capacitors in electronic equipment are different: the electrostatic coupling between their plates is extremely strong, the electrostatic coupling to the earth is nearly zero, and the current in the terminals connected to the two plates is always equal. The charge on their plates MUST be equal and opposite, always. But in physics textbooks, you can have three coulombs on one metal sphere, and two coloumbs on another.

Here is an "electrical engineering" way to understand it. Suppose the capacitance between two parallel plates is X microfarads. Suppose we force some charge into one plate, but we do not connect the other plate to anything. In this case, the lines of electric force extend outwards from both plates to the earth. Important question: what is the capacitance of the "capacitor" formed by one plate and the distant earth? It is small. VERY small, possibly millions or even billions of times smaller than the number of microfarads existing between the two plates. Therefore, if we connect both capacitor terminals to a circuit and force charges "through" this capacitor, the voltage across the plates will rise slowly, but if we instead try to force the same current into only ONE plate (and leave the second plate disconnected), then the voltage between the capacitor and the earth will rise millions or billions of times faster for the same current. In other words, a two-plate capacitor has immensely more capacitance than a one-plate capacitor. In electronics we usually ignore the "one-plate" phenomena entirely, and imagine that capacitors are a strange kind of two-terminal conductor.

Here is a model which exposes the problem. Rather than imagining a capacitor to be like two metal spheres, imagine it to be like one sphere which is divided into two parts, where the gap between the two parts is extremely small, and the capacitance value between the two parts is far larger than the capacitance value measured between each part and the distant earth...

             ____  ____
          __/    ||    \__
         /       ||       \
       /         ||         \       "Engineer's Capacitor"
      |          ||          |        
     |           ||           |     A spilt metal sphere with
    |            ||            |    a very narrow gap between 
    |            ||            |    the two halves
    |            ||            |
     |           ||           |
      |          ||          |
       \         ||         /
         \__     ||     __/
            \____||____/

           ______                ______
          /      \              /      \       The "Physicist's Capacitor"
        /          \          /          \
       |            |        |            |     Two separate metal spheres
      |              |      |              |
      |              |      |              |
       |            |        |            |
        \          /          \          /
          \______/              \______/

In my experience, the the two spheres of the "physicist's capacitor" cause distortion in physicists' concept of what the electronic component called "capacitor" really is.

Analogy: if we were talking about coils, how would physicists visualize electric transformers? They'd be very familiar with induced currents between pairs of distant air-core coils, yet they would be almost entirely unaware of of the strange effects arising with closely coupled coils of an iron core transformer. Power transformers behave very differently than two widely-spaced air-core inductors. The above split-sphere "engineer's capacitor" is analogous to an iron-core transformer, while the "two-sphere capacitor" of the physics textbooks is analogous to a pair if widely separated coils. When the coupling between the two parts approaches 100%, everything starts acting very differently.