A Variational Approach to Electrostatics of Polarizable Heterogeneous Substances
We discuss equilibrium conditions for heterogeneous substances subject to electrostatic or magnetostatic effects. We demonstrate that the force-like aleph tensor ℵij and the energy-like beth tensor ℶij for polarizable deformable substances are divergence-free: ∇iℵij=0 and ∇iℶij=0. We introduce two...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/659127 |
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| Summary: | We discuss equilibrium conditions for heterogeneous substances subject
to electrostatic or magnetostatic effects. We demonstrate that the
force-like aleph tensor ℵij and the energy-like beth tensor ℶij for polarizable
deformable substances are divergence-free: ∇iℵij=0 and ∇iℶij=0.
We introduce two additional tensors: the divergence-free energy-like gimel
tensor ℷij for rigid dielectrics and the general electrostatic gamma tensor Γij which is not divergence-free.
Our approach is based on a logically consistent extension of the Gibbs
energy principle that takes into account polarization effects. While the
model is mathematically rigorous, we caution against the assumption that
it can reliably predict physical phenomena. On the contrary, clear models
often lead to conclusions that are at odds with experiment and therefore
should be treated as physical paradoxes that deserve the attention of the
scientific community. |
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| ISSN: | 1687-9120 1687-9139 |