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Meaning of Zero Charge boundary condition (AC/DC)
Posted Jan 14, 2020, 7:33 a.m. EST Electromagnetics, Low-Frequency Electromagnetics Version 5.5 3 Replies
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Hello everyone!
Please help me understand the physical meaning of the Zero Charge boundary condition (BC) in electrostatics. While it is clear that constant/floating potential BC corresponds to a conductor surface, I can't figure out a similar correspondence for the "opposite" Zero Charge BC. The manual says:
".... This is the default boundary condition at exterior boundaries. At interior boundaries, it means that no displacement field can penetrate the boundary and that the electric potential is discontinuous across the boundary"
Why is it the default condition at exterior boundaries? Does it mimmic unbounded space? In what way?
Using this BC at interior boundaries leads to the electric field being tangential and "flowing around" an object with equipotential lines (in 2D) being normal to its surface. What kind of material should behave like this? It is neither conductor nor dielectric. A metamaterial?? What is the meaning of discontinuous potential at this boundary??
There is also a short relevant discussion in the description of "capacitor_fringing_fields" model which says that this BC "...can be treated as a perfectly insulating surface, across which charge cannot redistribute itself" But I still cannot understand what kind of insulation we are speaking about here, physically.
Many thanks for taking care to educate me (and perhaps some other unexperienced users). There must be a simple physical answer, but I just cannot find it on the web or in textbooks.
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Antonny,
I think it should rather be seen as a symmetry boundary condition than as something related to a physical material. I also have some difficulties to see where it could be useful as an internal boundary. It is not really meant to represent a boundary into open space but can be good enough if the electric field is small at the outer boundary relative to the region of interest. If you need to have a better approximation for open space you should use infinite element domains.
Cheers Edgar
-------------------Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
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If you are doing an electrostatic model of a finite sized region containing variously separated charges (or charged objects, or conductors at various potential differences such as capacitor plates), but (and this is important!) which has no net overall charge, then the outward (radial, if a sphere) component of the electric field must fall off very rapidly with distance from those objects, since there is no monopole term (only dipole or higher terms). This is actually a fairly common situation. A conceptual surrounding computational-volume boundary, such as a sphere (or similar) with any modest radius away from all those objects will thus have a relatively-low component of E normal to its surface. After all, the electric field lines associated with the dipole and higher order terms are (except for certain symmetry points) all closed. Since you have no choice but to work with a finite-sized computational volume, it is a reasonable approximation to assume the field at the computational boundary (again, if it is far enough away from the charges) will be (nearly) tangential to E at most/all points of interest. And that is the "zero charge" boundary condition. At least, that is what I use it for.
-------------------Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
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Dear Edgar and Robert,
Many thanks for your clarification! It all makes more sense now, especially why this condition is the default choice for external boundaries. I should have figured it out myself, actually, but those simple examples that I played with when trying to understand this kind of BC were all monopole. And for them Zero Charge external boundary condition is not at all "natural".
Still I seem to be missing some important physical points about the relation between this boundary being "zero charge" and "perfectly insulating". There is zero charge everywhere in an electrostatic model unless explicitly prescribed, right? Or may it be that there is no physical meaning that I am searching for (at least for electrostatics), and we can only talk about "mathematically" insulating boundary across which electric field cannot penetrate? (Like, for example, if it were not electric field, but a flow of a liquid it would be the other way around. Tangential velocity around an object would make perfect physical sense, while it being normal to the surface of an object would be much more difficult to interpret physically)
There seems to be another useful discussion here: http://www.kirbyresearch.com/index.cfm/wrap/textbook/microfluidicsnanofluidicsse22.html But they are talking about electrodynamics and still I don't quite get the point.