Biological fluids are water-based, ionic conductors. As such, they have both high relative dielectric constants and substantial conductivities, meaning they are lossy dielectrics. These fluids contain charged molecules (free charges), whose movements play roles in essentially all cellular processes from metabolism to communication with other cells. Using the problem of a point source in air above a biological fluid of semi-infinite extent, the bound charges in the fluid are shown to perform the function of a fast-acting Faraday cage, which protects the interior of the fluid from external electric fields. Free charges replace bound charges in accordance with the fluid's relaxation time, thereby providing a smooth transition between the initial protection provided by the bound charges and the steady state protection provided by the free charges. The electric fields within the biological fluid are thus small for all times just as they would be inside a classical Faraday cage.
REFERENCES
1.
Walter
Bernardi
, “The Controversy on Animal Electricity in Eighteenth-Century Italy: Galvani, Volta and Others
,” in Nuova Voltiana
, edited by F.
Bevilacqua
and L.
Fregonese
(Hoepli
, Milano
, 2000
), Vol. I
, pp. 101
–114
.2.
Nahum
Kipnis
, “Changing a Theory: The Case of Volta's Contact Electricity
,” in Volta and the History of Electricity
, edited by F.
Bevilacqua
and E.
Giannetto
(Hoepli
, Milano
, 2003
), pp. 17
–35
.3.
Semi-infinite volumes are also referred to as “half-spaces.” See
Arnold
Sommerfeld
, Electrodynamics: Lectures on Theoretical Physics
, Vol. III
(Academic Press
, New York, NY
, 1964
), p. 63
.4.
William
Ralph Bennett
, Jr., Health and Low-Frequency Electromagnetic Fields
(Yale University Press
, New Haven, CT
, 1994
), p. 92
.5.
World Health Organization (WHO), “
What Are Electromagnetic Fields?
,” <http://www.who.int/peh-emf/about/WhatisEMF/en/index3.html>.6.
W. J.
Koshak
, E. P.
Krider
, N.
Murray
, and D. J.
Boccippio
, “Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison with LIS Satellite Data
,” J. Atmos. Oceanic Technol.
24
, 1817
–1838
(2007
).7.
See
Robert
Plonsey
, Bioelectric Phenomena
, (McGraw-Hill
, New York, NY
, 1969
), p. 182
, where a transmembrane potential of 1.0 mV across a membrane having a specific capacitance of 1 μF/cm2 is shown to correspond to a charge density of 10−9 C/cm2. For a spherical cell having a diameter of 50 μ and a resting potential of 100 mV (inside negative), this charge density corresponds to a total charge of 7.8 × 10−12 C on each of the intracellular and extracellular surfaces of the membrane, negative on the inside and positive on the outside.8.
T. J.
Tucker
, “Spark initiation requirements of a secondary explosive
,” Ann. New York Acad. Sci.
152
, 643
–653
, (1968
);Michel
Mardiguian
, Electro Static Discharge: Understand, Simulate, and Fix ESD Problems
, (John Wiley & Sons
, New York, NY
, 2011
).9.
David J.
Griffiths
, Introduction to Electrodynamics
, 3rd ed. (Prentice-Hall
, Upper Saddle River, NJ
, 1999
), p. 101
.10.
See, for example,
James Clerk
Maxwell
, A Treatise on Electricity and Magnetism
, unabridged 3rd ed., published by Clarendon Press in 1891, Vol. 1
(Dover Publications Inc.
, Mineola, NY
, 1954
), pp. 252
–253
;James H.
Jeans
, The Mathematical Theory of Electricity and Magnetism
, 5th ed. (Cambridge U.P.
, London, England
, 1933
), pp. 183
–187
and 200–201;Julius Adams
Stratton
, Electromagnetic Theory
(McGraw-Hill
, New York, NY
, 1941
), pp. 193
–194
; Sommerfeld, Ref. 3, pp. 63–64;Edward M.
Purcell
, Electricity and magnetism
, Berkeley Physics Course, Vol. 2
(McGraw-Hill
, New York, NY
, 1965
), pp. 92
–94
;Markus
Zahn
, Electromagnetic Field Theory: A Problem Solving Approach
(John Wiley & Sons Inc.
, New York, NY
, 1979
), pp. 107
–109
and 164–165;Oleg D.
Jefimenko
, Electricity and Magnetism: An Introduction to the Theory of Electric and Magnetic Fields
, 2nd ed. (Electret Scientific Company
, Star City, WV
, 1989
), pp. 161
–165
and 244–245; Griffiths, Ref. 9, pp. 121–124 and 188–190.11.
As used herein, σcon is the conductivity of the biological fluid, and σb and σf are the surface charge densities of bound and free charges, respectively, at the biological fluid's surface.
12.
Kenneth R.
Foster
and Herman P.
Schwan
, “Dielectric Properties of Tissues
,” in CRC Handbook of Biological Effects of Electromagnetic Fields
, edited by Charles
Polk
and Elliot
Postow
(CRC Press
, Boca Raton, FL
, 1986
), p. 88
; Bennett, Ref. 4, p. 106.13.
Purcell, Ref. 10, p. 341.
14.
Ruth W.
Chabay
and Bruce A.
Sherwood
, Matter and Interactions
, 3rd ed. (John Wiley & Sons Inc.
, New York, NY
, 2011
).15.
W. G. V.
Rosser
, “Magnitudes of surface charge distributions associated with electric current flow
,” Am. J. Phys.
38
(2
), 265
–266
(1970
).16.
J. D.
Jackson
, “Surface charges on circuit wires and resistors play three roles
,” Am. J. Phys.
64
(7
), 855
–870
(1996
).17.
Norris W.
Preyer
, “Surface charges and fields of simple circuits
,” Am. J. Phys.
68
(11
), 1002
–1006
(2000
).18.
For reviews see Bennett, Ref. 4; Polk and Postow, Ref. 12;
Jaakko
Malmivuo
and Robert
Plonsey
, Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields
(Oxford U.P.
, New York
, 1995
);Richard H. W.
Funk
, Thomas
Monsees
, and Nurdan
Özkucur
, “Electromagnetic effects— From cell biology to medicine
,” Prog. Histochemistry and Cytochemistry
43
, 177
–264
(2009
);David
Hafemeister
, “Resource Letter BELFEF-1: Biological Effects of Low-Frequency Electromagnetic Fields
,” Am. J. Phys.
64
(8
), 974
–981
(1996
).19.
See also
A.
Herczyński
, “Bound charges and currents
,” Am. J. Phys.
81
(3
), 202
–205
(2013
).20.
Representative examples include Maxwell, Ref. 10, p. 451; Jeans, Ref. 10, pp. 359–360; Stratton, Ref. 10, p. 15; Zahn, Ref. 10, p. 182; Jefimenko, Ref. 10, p. 498.
21.
W. M.
Saslow
and G.
Wilkinson
, “Expulsion of Free Electronic Charge from the Interior of a Metal
,” Am. J. Phys.
39
(10
), 1244
–1248
(1971
);Neil
Ashby
, “Relaxation of charge imbalances in conductors
,” Am. J. Phys.
43
(6
), 553
–555
(1975
);Hans C.
Ohanian
, “On the approach to electro- and magneto-static equilibrium
,” Am. J. Phys.
51
(11
), 1020
–1022
(1983
);V. V.
Paranjape
, “On return to thermal equilibrium for the excess charge distribution in semiconductors
,” Am. J. Phys.
53
(4
), 355
–357
(1985
).22.
Purcell, Ref. 10, p. 140.
23.
Saslow and Wilkinson, Ref. 21; Ohanian, Ref. 21.
24.
Mituo
Uehara
et al, “Physics and Biology: Bio-plasma physics
,” Am. J. Phys.
68
(5
), 450
–455
(2000
).25.
John
Bockris
and Amulya
Reddy
, Modern Electrochemistry, Volume 1: Ionics
(Plenum Press
, New York, NY
, 1998
), p. 46
.26.
Bockris and Reddy, Ref. 25, p. 66.
27.
Ashby, Ref. 21, p. 553;
Donald E.
Tilley
, “Drift speed and collision time
,” Am. J. Phys.
44
(6
), 597
–598
(1976
).28.
When inserted in Eq. (7), these values for mNa and mCl give transport numbers (transference numbers) of 0.43 and 0.57 for sodium and chlorine, in substantial agreement with the published values of 0.39 and 0.61. Bockris and Reddy, Ref. 25, p. 478.
29.
Zahn, Ref. 10, pp. 184–189.
30.
Markus
Zahn
, Electromagnetic Field Theory: A Problem Solving Approach
, Spring
2008
, RES.6-002, Massachusetts Institute of Technology: MIT OpenCourseWare, <http://ocw.mit.edu/resources/res-6-002-electromagnetic-field-theory-a-problem-solving-approach-spring-2008/textbook-contents/> (Accessed 4 Oct, 2013). License: Creative Commons BY-NC-SA.31.
Solutions to the layered, lossy capacitor problem can also be found in
Hermann A.
Haus
, James R.
Melcher
, Markus
Zahn
, and Manuel L.
Silva
, Electromagnetic Fields and Energy
(Prentice-Hall
, Englewood Cliffs, NJ
, 1989
) and Massachusetts Institute of Technology: MIT OpenCourseWare, RES.6-001, Electromagnetic Fields and Energy, Spring 2008, <http://ocw.mit.edu/resources/res-6-001-electromagnetic-fields-and-energy-spring-2008> (Accessed 4 Oct, 2013). License: Creative Commons BY-NC-SA, Chap. 7, pp. 47–50, as well as in Maxwell, Ref. 10, pp. 452–458.32.
Purcell, Ref. 10, pp. 340–342.
33.
Purcell, Ref. 10, pp. 341–342.
34.
See, for example,
Thomas
Meissner
and Frank J.
Wentz
, “The Complex Dielectric Constant of Pure and Sea Water From Microwave Satellite Observations
,” IEEE Trans. Geosci. Remote Sensing
42
(9
), 1836
–1849
(2004
).35.
Plonsey, Ref. 7, p. 205.
36.
Bertil
Hille
, Ion Channels of Excitable Membranes
, 3rd ed. (Sinauer Associates Inc.
, Sunderland, MA
, 2001
), p. 577
.37.
Foster and Schwan, Ref. 12, pp. 88-91.
38.
Th.
Heubrandtner
, B.
Schnizer
, and W.
Riegler
, “The Quasi-static Approximation for Weakly Conducting Media and Applications
,” in Proceedings of the 11th International IGTE Symposium
, pp. 138
–143
(2004
).39.
I. V.
Timoshkin
, S. J.
MacGregor
, R. A.
Fouracre
, B. H.
Crichton
, and J. G.
Anderson
, “Transient electrical field across cellular membranes: pulsed electric field treatment of microbial cells
,” J. Phys. D
39
, 596
–603
(2006
).40.
I. W.
McAllister
and G. C.
Crichton
, “Analysis of the temporal electric fields in lossy dielectric media
,” IEEE Trans. Electr. Insul.
26
(3
), 513
–528
(1991
).41.
This study treats the biological fluid as a homogeneous conductor as opposed to a bio-plasma where the concentrations of the individual ion species that carry the current are taken into account. See Uehara et al., Ref. 24;
see also
Bernard
Roulet
and Michel
Saint Jean
, “Image charges revisited: Beyond classical electrostatics
,” Am. J. Phys.
68
(4
), 319
–324
(2000
).42.
Griffiths, Ref. 9, p. 189.
43.
Griffiths, Ref. 9, p. 89, n6;
see also
Taro
Sometani
and Kenroku
Hasebe
, “Method for solving electrostatic problems having a simple dielectric boundary
,” Am. J. Phys.
45
(10
), 918
–921
(1977
).44.
Griffiths, Ref. 9, p. 186.
45.
John
David Jackson
, Classical Electrodynamics
, 3rd ed. (John Wiley & Sons Inc.
, New York, NY
, 1999
), p. 157
, Eq. (4.47).46.
Norris W.
Preyer
, “Transient behavior of simple RC circuits
,” Am. J. Phys.
70
(12
), 1187
–1193
(2002
).47.
Maurice M.
Klee
, “Charge distributions that cause current to enter a pore in a biological membrane
,” in Conf. Proc IEEE Eng. Med. Biol. Soc.
, pp. 1209
–12
(2007
).48.
Eq. (45) can also be obtained from image theory.
49.
Bennett, Ref. 4, pp. 107–114; Sommerfeld, Ref. 10, pp. 60–62; Jefimenko, Ref. 10, p. 244; Timoshkin, Ref. 39.
50.
Erwin
Neher
, “Nobel Lecture: Ion channels for communication between and within cells
,” EMBO Journal
11
(5
), 1673
–1679
(1992
);Bert
Sakmann
, “Nobel Lecture: Elementary steps in synaptic transmission revealed by currents through single ion channels
,” EMBO J.
11
(6
), 2003
–2016
(1992
).51.
Hille, Ref. 36, Chaps. 3, 19, and 20.
© 2014 American Association of Physics Teachers.
2014
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
