In Chapter 9 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss how well an external electric field penetrates the human body. We examine a sinusoidally varying field, but another problem is an field that turns on suddenly and then remains constant (a step function). This case is analyzed by Maurice Klee in his American Journal of Physics article “ Biology’s Built-In Faraday Cages” (Volume 82, Pages 451–459, 2014). Klee obtained a PhD in Biomedical Engineering from Case Western Reserve University, under the direction of Robert Plonsey, and a law degree from George Washington University. His abstract states
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.
The most interesting part of this article is the interplay between bound and free charges at the tissue surface. Klee assumes that bound charge, arising primarily from the rotation of the polarized water molecules, responds to the external electric field instantaneously, while free charge responds with a delay. The rapid bound charge shields the tissue immediately, but incompletely. Over time the free charge replaces the bound charge, eventually providing complete shielding of the tissue from the external electric field.
Klee addresses two questions: how completely does the bound charge shield the tissue, and how fast does the free charge replace the bound charge? (1) He shows that the initial bound charge is less than the final free charge by a factor of (κ — 1)/(κ + 1), where κ is the dielectric constant. Klee uses the value of 80 for κ, and finds that the bound charge provides 97.5% of the shielding that the free charge ultimately contributes. Russ and I point out that the dielectric constant of tissue can be much greater than water, and suggest a value of one million might be more appropriate. (2) The time constant for free charge to replace bound charge is κεo/ σ, where εo is the permittivity of free space and σ is the conductivity. If you use σ =0.5 S/m and κ = 80, the time constant is 1.4 nanoseconds. If you use κ = 1,000,000, the time required for complete shielding by the free charge is much longer (about 2 microseconds) but the initial shielding from the bound charge is 99.9998% complete.
Klee concludes that
Through a combination of bound and free charges, a biological fluid surrounded by a non-conductor of low relative dielectric constant does not develop large internal electric fields as a result of charges located outside the fluid. The fluid is thus its own robust Faraday cage, thereby ensuring that biological molecules within the fluid do not experience large electric fields due to outside sources.