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From: John Denker <email@example.com>
Sent: Thursday, February 25, 2021 10:30 PM
To: Jeffrey Schnick
Subject: Re: [Phys-L] non-polarized capacitor
On 2/25/21 7:56 PM, you wrote:
Do you accept the idea that the circuit with the diodes is aIt is a good model for our purposes. I used it to prove that the central conductor acquires a negative charge.
faithful model of the circuit with the non-ideal electrolytics?
If the central node had an appreciable number of field lines spewingAgreed.
out in all directions and terminating at infinity (or on the chassis),
like the pole of a van de Graaf generator, then it would be a clear
violation of the Kirchhoff "laws" ... but it doesn't. 99.999% of the
charge associated with the central node is inside the capacitors.
The field lines go from plate to plate. This keeps Kirchhoff happy.I agree with the first sentence, not the second. Let's establish a gaussian surface that encloses the central conductor and nothing else. It encloses one plate from each capacitor and the wire connecting those two plates. Prior to application of the source voltage, both capacitors have 0 gorge and 0 charge. The net outward flux through the gaussian surface is zero. The charge enclosed by the gaussian surface is zero. Now we connect the oscillatory voltage source to the system and let it run until there is no more leakage current. From then on, one or both of the capacitors has non-zero gorge. Whenever the upper capacitor has gorge, there is an electric field in the region between its plates and that electric field is directed from the top plate toward the bottom plate, thus inward through the gaussian surface. Whenever the lower capacitor has gorge, there is an electric field in the region between its plates and that electric field is directed from the bottom plate toward the top plate, thus inward through the gaussian surface. The flux through the gaussian surface at points outside the two regions just discussed (I am aware of the fringing nitpick that could be made here but the argument still holds with fringing taken into account) is negligible. The net flux through the gaussian surface is thus inward. Thus, there is a net negative charge inside the gaussian surface. The only thing inside the gaussian surface is the central conductor, so, the central conductor has a net negative charge. There is no field-line concentration exception to Gauss's law. There is charge on the central conductor even though the electric field is non-zero only in the regions between the two plates of each capacitor.
Again I say: This is just like any other circuit you could build.They all obey the same actual laws of physics.
Floating nodes are weird, and have to be analyzed carefully, but they'reI think I have analyzed this one with standard physics concepts, carefully applied.
not so weird that we can't analyze them with standard concepts, carefully
Would it help to clip out one of the capacitors?I don't think so.
Would it help to remove the diodes and instead use a battery and aPresetting the voltage of the central conductor to −V_max/2 is neither necessary nor, in general, sufficient to make it so that when you apply the sinusoidal source voltage to the combo capacitor there is no transient phase. What you would have to do in advance is to put charge q <= −Q on the central conductor. You could do this by connecting the low side of a V_max battery to the central conductor and momentarily connecting the high side of that battery: to the top plate of the upper capacitor (thus leaving the preset voltage of the central node at 0), or, to the bottom plate of the lower capacitor (making the preset voltage of the central node −V_max). Or, you could connect the low side of a V_max/2 battery to the central conductor and momentarily touch the high side to both the top of the upper capacitor and the bottom of the lower capacitor, either simultaneously or in turn (this would make the preset voltage of the central node −V_max/2 which, I think, is the value you had in mind). In both cases, you can use a higher voltage battery than specified just above, thus putting some extra negative charge on that central conductor; the extra negative charge will just sit there as a uniform charge distribution on the central conductor once you apply the sinusoidal source voltage that oscillates between −V_max and V_max; only −Q of the charge will surge up and down from one end of the central conductor to the other. Note that if, starting with everything neutral (and the diodes in the circuit, or, with the capacitors being electrolytics), you preset the voltage of the central conductor simply by momentarily connecting the low side of a V_max/2 battery to the central conductor and the high side to the bottom of the lower capacitor, you would only put a charge of −Q/2 on the central conductor and once you removed the battery and applied the sinusoidal source voltage there would be transient current until the charge on the central conductor got to be −Q.
high-value resistor to charge up the central node to −⌈V⌉/2 at some
ancient time, before the capacitor-pair gets used? Then you don't
have a floating node at all.