PNP what is in a name july 25-1 2019.pdf 10.31224/osf.io/2739d

Eisenberg, Robert S.

doi:10.31224/osf.io/2739d

“…It is not at all clear that Maxwell’s equations joined with constitutive equations; and boundary conditions always have steady state solutions in the sinusoidal case. The Maxwell equations joined with diffusion and convection equations (like Navier–Stokes [ 118 , 119 , 120 , 121 , 122 , 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 , 131 , 132 , 133 , 134 , 135 ] or PNP

Poisson Nernst Planck

drift diffusion [ 52 , 53 , 55 , 57 , 59 , 61 , 123 , 136 , 137 , 138 , 139 , 140 , 141 , 142 , 143 , 144 , 145 ]) certainly do not always have solutions that are linear functions of just the electric field [ 146 , 147 , 148 , 149 ].”…”

Section: Discussion: From Electrodynamics To Biophysics and Backmentioning

confidence: 99%

Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Eisenberg

¹

2021

Entropy

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When forces are applied to matter, the distribution of mass changes. Similarly, when an electric field is applied to matter with charge, the distribution of charge changes. The change in the distribution of charge (when a local electric field is applied) might in general be called the induced charge. When the change in charge is simply related to the applied local electric field, the polarization field P is widely used to describe the induced charge. This approach does not allow electrical measurements (in themselves) to determine the structure of the polarization fields. Many polarization fields will produce the same electrical forces because only the divergence of polarization enters Maxwell’s first equation, relating charge and electric forces and field. The curl of any function can be added to a polarization field P without changing the electric field at all. The divergence of the curl is always zero. Additional information is needed to specify the curl and thus the structure of the P field. When the structure of charge changes substantially with the local electric field, the induced charge is a nonlinear and time dependent function of the field and P is not a useful framework to describe either the electrical or structural basis-induced charge. In the nonlinear, time dependent case, models must describe the charge distribution and how it varies as the field changes. One class of models has been used widely in biophysics to describe field dependent charge, i.e., the phenomenon of nonlinear time dependent induced charge, called ‘gating current’ in the biophysical literature. The operational definition of gating current has worked well in biophysics for fifty years, where it has been found to makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that the operational definition of gating current be used to define voltage and time dependent induced charge, although other definitions may be needed as well, for example if the induced charge is fundamentally current dependent. Gating currents involve substantial changes in structure and so need to be computed from a combination of electrodynamics and mechanics because everything charged interacts with everything charged as well as most things mechanical. It may be useful to separate the classical polarization field as a component of the total induced charge, as it is in biophysics. When nothing is known about polarization, it is necessary to use an approximate representation of polarization 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.

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Circuits, Currents, Kirchhoff, and Maxwell

Eisenberg

¹

2023

Qeios

1

0

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Electricity flows in circuits that bring us power and information. The current flow in circuits is defined by the Maxwell equations that are as exact and universal as any in science. The Maxwell-Ampere law defines the source of the magnetic field as a current. In a vacuum, like that between stars, there are no charges to carry that current. In a vacuum, the source of the magnetic field is the displacement current, \(\varepsilon_0\ \partial\mathbf{E}/\partial t\). Inside matter, the source of the magnetic field is the flux of charge added to the displacement current. This total current obeys a version of Kirchhoff’s current law that is implied by the mathematics of the Maxwell equations, and therefore is as universal and exact as they are. Kirchhoff's laws provide a useful coarse graining of the Maxwell equations that avoids calculating the Coulombic interactions of \({10}^{23}\) charges yet provide sufficient information to design the integrated circuits of our computers. Kirchhoff's laws are exact, as well as coarse grained because they are a mathematical consequence of the Maxwell equations, without assumption or further physical content. In a series circuit, the coupling in Kirchhoff’s law makes the total current exactly equal everywhere at any time. The Maxwell equations provide just the forces needed to move atomic charges so the total currents in Kirchhoff’s law are equal for any mechanism of charge movement. Those movements couple processes for any physical mechanism of charge movement. In biology, Kirchhoff coupling is an important part of membrane transport and enzyme function. For example, it helps the membrane enzymes cytochrome c oxidase and ATP-synthase produce ATP, the biological store of chemical energy.

show abstract

Circuits, Currents, Kirchhoff, and Maxwell

Eisenberg

¹

2023

Qeios

0

View full text Add to dashboard Cite

Electricity flows in circuits that bring us power and information. The current flow in circuits is defined by the Maxwell equations that are as exact and universal as any in science. The Maxwell-Ampere law defines the source of the magnetic field as a current. In a vacuum, like that between stars, there are no charges to carry that current. In a vacuum, the source of the magnetic field is the displacement current, \(\varepsilon_0\ \partial\mathbf{E}/\partial t\). Inside matter, the source of the magnetic field is the flux of charge added to the displacement current. This total current obeys a version of Kirchhoff’s current law that is implied by the mathematics of the Maxwell equations, and therefore is as universal and exact as they are. Kirchhoff's laws provide a useful coarse graining of the Maxwell equations that avoids calculating the Coulombic interactions of \({10}^{23}\) charges yet provide sufficient information to design the integrated circuits of our computers. Kirchhoff's laws are exact, as well as coarse grained because they are a mathematical consequence of the Maxwell equations, without assumption or further physical content. In a series circuit, the coupling in Kirchhoff’s law makes the total current exactly equal everywhere at any time. The Maxwell equations provide just the forces needed to move atomic charges so the total currents in Kirchhoff’s law are equal for any mechanism of charge movement. Those movements couple processes for any physical mechanism of charge movement. In biology, Kirchhoff coupling is an important part of membrane transport and enzyme function. For example, it helps the membrane enzymes cytochrome c oxidase and ATP-synthase produce ATP, the biological store of chemical energy.

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PNP what is in a name july 25-1 2019.pdf 10.31224/osf.io/2739d

Cited by 4 publications

References 65 publications

Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Circuits, Currents, Kirchhoff, and Maxwell

Circuits, Currents, Kirchhoff, and Maxwell

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