Discussion Forum

First, you need to fix the potential on both plates, not let anything float. For the best results, arrange your two plates centered, symmetrically, inside a grounded (V=0) container that is quite large compared to the plates, so it does not interfere significantly with the fields between them. For convenience, put +0.5V on one plate and -0.5V on the other. This yields a potential difference of 1V and a far-away potential ~ 0, so the aforementioned distant external grounded boundary won't matter much. Make sure your mesh isn't too coarse. Now solve the problem (using the electrostatics module, of course). Now, we simply use the fact that C = Q/V where Q = total charge on one plate (use the positive one, to get the sign right) and V = voltage between them (which is already = 1 V). So now all you need to do is integrate the surface charge density over one of the plates (use the positive one, as already noted) and that will give you the capacitance.

Note: You can employ symmetry planes if you wish, to speed up the computations, but you will need to think it through to understand when or when not to include various factors of 2. Note that for two differently shaped conductors, this approach still works. The magnitude of the integrated surface charge on either conductor will always be identical, so you still find C by computing Q/V.

2nd comment:

Oops, I see that my answer was more applicable to the earlier version of Comsol Multiphysics! But you can still do it the way I suggested. However, in the newer version, there is evidently a capacitance computation built-in that I can only suppose is intended to make this process easier. ...But I confess that I haven't tried this particular new tool yet! Best regards. :-)

Thank you so much.

My problem is a little complicated. I need to calculate the capacitance between a float object and the electrode. Basically, I have four parallel plates. I did the following steps:

1. I set four parallel plates. The bottom plate (copper) is ground with 3'' * 3'' * 0.1''. The middle (second and third) two plates (copper) are electrode (because I need to put a PCB board between this two plates) with 2'' * 2'' * 0.1'' and electric potential 5V. The top plate is object (silicon) which is 1'' * 1'' * 0.1'' which need to be floated.
(HENCE, basically it can look as three parallel plates: top=object, middle tow plates= electrode, bottom = ground)

2. I set a very big box as a container and with metarial air.

I have meshed everything and it works. However, I want to calculate the capacitance between object and electrode.

I used global evaluation to evaluate capacitance. It only has es.C11 which I think is the self capacitance for electrode.

How can I calculate the capaciatnce between object (top plate) and electrode (second plate).?

I have attached my simulation file. Can you take a look?

Thanks,

Shengan,

This problem is linear, so the capacitance between any two conductors is independent of whether those conductors are floating or are assigned potentials. The capacitance depends only on the geometry and the dielectrics. So you can still solve the problem the way I said before. Specifically, pick any two of the conducting surfaces and assign them the potentials +.5V and -.5V and then proceed as before, letting all the other surfaces float. You can set up and solve for each capacitance pair separately, by simply changing which surfaces you assign potentials and which surfaces float. (Now, if some of those surfaces are always going to float, there may not be much reason to *care* about the capacitances that involve them, but that is a separate question.)

Hi Robert,

The thing is now our group trying to develop a proximity sensors to be used on mobile MRI systems. I know it's a slight capacitance between a floating object and electrode. However, I still want know the capacitance change due to distance increase between floating object and the electrode.

So you mean I still can give a potential for the floating plate(object)? However, I think the capacitance between the object and electrode wll change if I give a potential (eg: 5v for electrode and -5v for object) compare with floating the object. For my question, the object need to be always floating.

Thanks,

Jeff

Whether you choose to apply any particular potential to any particular electrode or not does not affect the capacitance between any two electrodes, unless you have some kind of unusual voltage-dependent capacitor (such as one with a ferroelectric in it). I have simply described a procedure that you can use to determine the capacitance between any two electrodes. Neither the procedure, nor the result of it, depend on whether you ultimately/later choose to let either or both of the electrodes float or not, since that has nothing to do with the definition of the capacitance between them. To make this clearer, note that you can buy a capacitor at any electronics store and find its capacitance marked right on it (e.g., "10 pF"). That doesn't mean that it is only a 10 pF capacitor if you happen to charge it to a certain voltage, or bias one or both of the electrodes a certain way, etc. Rather, this capacitance has the meaning that when you apply a voltage difference V between the electrodes, this will lead to a charge of +Q being on one electrode and -Q on the other, and that the value of Q will be given by Q=CV, where C is the "capacitance." Now, whether or not the capacitance (between any two particular electrodes that may be part of a more complex system that you might have) is actually relevant and/or important to your particular work/problem, is a very different question. Maybe, for your application, considering the way you intend to apply your voltages, you need to know the capacitance between some particular pair of electrodes or maybe you don't. That's for you, as the designer/analyst, to decide. But that doesn't affect the computation.

For more about capacitance, see (for example): en.wikipedia.org/wiki/Capacitance .

Another comment: If you actually intend to apply various potentials to 3 or more interacting electrodes at once, you *may* (or may not) be interested in the "capacitance matrix." Again, see en.wikipedia.org/wiki/Capacitance for more info. Good luck.