Version 1
: Received: 23 August 2020 / Approved: 25 August 2020 / Online: 25 August 2020 (13:38:14 CEST)
Version 2
: Received: 27 August 2020 / Approved: 28 August 2020 / Online: 28 August 2020 (08:44:51 CEST)
Eisenberg, R.S. Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics. Entropy 2021, 23, 172, doi:10.3390/e23020172.
Eisenberg, R.S. Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics. Entropy 2021, 23, 172, doi:10.3390/e23020172.
Eisenberg, R.S. Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics. Entropy 2021, 23, 172, doi:10.3390/e23020172.
Eisenberg, R.S. Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics. Entropy 2021, 23, 172, doi:10.3390/e23020172.
Abstract
Electrodynamics is usually written using polarization fields to describe changes in distribution of charge as electric fields change. This approach does not specify polarization fields uniquely from electrical measurements. Many polarization fields will produce the same electrodynamic forces and flows because only divergence of polarization enters Maxwell’s first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. To be unique, models must describe the charge distribution and how it varies. I propose a different paradigm to describe field dependent charge, i.e., the phenomenon of polarization. This operational definition of polarization has worked well in biophysics for fifty years, where a field dependent, time dependent polarization provides gating current that makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that operational definition be used to define polarization charge in general. Charge movement needs to be computed from a combination of electrodynamics and mechanics because ‘everything interacts with everything else’. The classical polarization field need not enter into that treatment at all. When nothing is known about polarization, it is necessary to use an approximate representation with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.
Copyright:
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