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Intermediate Physics for Medicine and Biology pp 239–268Cite as

Electricity and Magnetism at the Cellular Level

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Abstract

This chapter describes a number of topics related to charged membranes and the movement of ions through them, including Donnan equilibrium, the Gouy–Chapman model, and the Nernst–Planck equation. Ions in solution are analyzed using the Debye–Hückel model and the Poisson–Boltzmann equation. Membrane ion channels are then discussed, with an emphasis on the potassium ion channel structure and function. Patch clamp methods can be used to measure the electrical current through individual channels, but noise in these measurements often obscures the signal. The chapter ends with a review of the possible effects of weak electric and magnetic fields on the body.

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Notes

  1. 1.

    Throughout this section, we keep \(4\uppi \) in both numerator and denominator that could be canceled. We do this for two reasons. First, the quantity \(1/4\uppi \epsilon_0\) has a numerical value of about \(9\times 10^{9}\), which is easy to remember; second, for those who do not use SI units, the factor \(1/4\uppi \epsilon _0\) does not appear, but the other factor of \(4\uppi \) remains.

  2. 2.

    We have seen this equation before in electrotonus when the membrane capacitance is fully charged (Sect. 6.12).

  3. 3.

    A more sophisticated model for the alignment of the electric dipoles in the electric field is analogous to that for magnetic moments in Sect. 8.3.

  4. 4.

    We use \(x\) for the distance in the direction parallel to \(\mathbf {E}\) because \(z\) is used for valence.

  5. 5.

    For the detection of light, the amount of energy per photon is so much greater than \(k_{B}T\) that shot noise dominates.

  6. 6.

    Foster (1996) reviewed many of the laboratory studies and described cases where subtle cues meant the observers were not making truly “blind” observations. Though not directly relevant to the issue under discussion here, a classic study by Tucker and Schmitt (1978) at the University of Minnesota is worth noting. They were seeking to detect possible human perception of 60-Hz magnetic fields. There appeared to be an effect. For 5 years they kept providing better and better isolation of the subject from subtle auditory clues. With their final isolation chamber, none of the 200 subjects could reliably perceive whether the field was on or off. Had they been less thorough and persistent, they would have reported a positive effect that does not exist.

  7. 7.

    That is, the carcinogenic effects are in International Association for Research on Cancer group 2B (possibly carcinogenic), a group that includes coffee and pickled vegetables.

  8. 8.

    Readers who are familiar with the concepts of reactance and complex impedance must be frustrated because we have not used them. The reason is pedagogic. Because many in our intended audience may have had only one year of calculus, we want to avoid the use of complex numbers. In Chap. 11 we introduce them as a parallel notation. They are widely used in the image reconstruction described in Chap. 12.

  9. 9.

    Recall that the membrane time constant \(\tau \) was used in Eq. 6.40. The values of conductivity or resistivity and dielectric constant are different in this case.

  10. 10.

    Calculated using equations in Polk (1995), p. 62.

  11. 11.

    Each issue of the journal Medical Physics contains one Point/Counterpoint article, in which a proposition is stated and two prominent medical physicists debate it, one for and one against. You can download all the point/counterpoint articles at http://www.medphys.org. They are a great resource to use when teaching medical physics.

  12. 12.

    Wireless local area networks.

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Authors and Affiliations

  1. University of Minnesota, Minneapolis, Minnesota, USA

    Russell K. Hobbie

  2. Oakland University, Rochester, Michigan, USA

    Bradley J. Roth

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  1. Russell K. Hobbie
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Correspondence to Russell K. Hobbie .

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Hobbie, R., Roth, B. (2015). Electricity and Magnetism at the Cellular Level. In: Intermediate Physics for Medicine and Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-12682-1_9

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