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General Principles: Magnetically Induced Current

At frequencies below approximately one megahertz, most biological tissue can be modeled as a purely conducting medium, and secondary magnetic fields produced by currents in the tissue can be neglected. This means that the current induced by an alternating magnetic field can be calculated using only Faraday's law and Laplace's equation, without simultaneously solving all of Maxwell's equations (Stuchly, 1995). Estimating the induced current in an object of finite dimension is usually only possible using numerical simulations, but in certain extremely simple cases, the current distribution can be expressed analytically. For example, if the medium is assumed to be infinite and homogeneous, the current density in a circular path of radius r perpendicular to a sinusoidally varying magnetic field of frequency f is

J = PI S r B f

where J is the current density (in Amps/m²), S is the conductivity of the medium (in 1/(Ohm meters)), and B is the magnetic flux density (in Tesla).

At 10-100kHz, blood has been reported to have a conductivity of 0.55-0.68 1/(Ohm meters), while bone and brain tissue have conductivities of approximately 0.0133-0.0144 and 0.12-0.17 1/(Ohm meters), respectively (Foster, 1995). Thus, in an infinite conductor with the properties of brain tissue, a field of 100uT (microtesla) at 20kHz will induce a current density, in a circle of radius 10cm, of approximately 10 uA/cm². For comparison, stimulation of excitable cells requires peak currents at this frequency of more than 700 uA/cm² (IEEE, 1992), while ambient currents in the human body are typically less than 1 uA/cm² (IRPA, 1990) (and most of this energy is concentrated at extremely low frequencies).

Unfortunately, the value of estimates based on equation 1 is limited. In general, currents will depend more or less linearly on frequency, field strength, conductivity, and radius, as predicted by equation 1, but interfaces between different media in a heterogeneous object may cause the current at any particular frequency to be quite a bit different from that predicted by equation 1. Standards for maximum permissible exposure are typically based on computational and physical studies using realistic heterogeneous models of the human body.


next up previous
Next: Health Risks of Magnetic Up: Electromagnetic Exposure Safety of Previous: Electromagnetic Exposure Safety of

Mark Hasegawa-Johnson
Mon May 26 15:33:40 PDT 1997