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Electromagnetics
Published in Arun G. Phadke, Handbook of Electrical Engineering Calculations, 2018
Equations (2.12) and (2.13) are “exact” to the degree that kL ≪ 1 and are valid in the near field (except at r = 0) and the far field. Note that the magnetic field has only a φ component, a result to be expected from our knowledge of statics, where a straight filament of current was found to have only an azimuthal magnetic field. But in addition to the static (i.e., frequency-independent) 1/r2 term that is predicted by the Biot–Savart law, there is a 1/r term whose magnitude is proportional to frequency via k = ω/c, with c the speed of light. The electric field similarly has not only the radial component that can be anticipated from a stationary point charge, but a θ component as well, whose magnitude is also proportional to frequency. These k-dependent components obviously arise from the oscillatory nature of the Hertzian dipole current, and can be deduced to be associated with electromagnetic radiation, as each is proportional to 1/r.
Introduction to Instrumentation
Published in Christakis Constantinides, Magnetic Resonance Imaging, 2016
Both the gradient coils and the radio frequency coils (as will be discussed in Sections 7.4.1–7.4.3 and 7.5) can use the Biot–Savart law to compute the magnetic field distribution. For a magnetic field in three-dimensional space B(r), generated by a unit length of a conductor δl, carrying a current I, Biot–Savart states that for any point in space P(x, y, z) the magnetic field is given by () B(r)=μoI4π∮dl×(r−r′)|r−r′|3dr where μο is the magnetic permeability and r and r′ are the distances of the conducting wire and the point in space for which the magnetic field is being computed, respectively.
Growth alteration of Allium cepa L. roots exposed to 1.5 mT, 25 Hz pulsed magnetic field
Published in International Journal of Environmental Health Research, 2022
Alejandro González-Vidal, Silvia Mercado-Sáenz, Antonio M. Burgos-Molina, Francisco Sendra-Portero, Miguel J. Ruiz-Gómez
The value of the low-frequency MF associated with the voltage waveform is proportional to the level of current intensity in a circuit (Law of Biot-Savart), and its time derivative has the same waveform as the electromotive force in a pickup coil in air (Faraday’s Law of electromagnetic induction). The waveform of the time derivative of the current intensity in the circuit (the same waveform as the time derivative of the MF) was measured with a pickup coil in air, being tested that it was according to the temporal variation of the current intensity in an inductive circuit. According to Faraday’s Law of Induction, a time varying MF will induce an electric field according to the equation:
Exposure of S. cerevisiae to pulsed magnetic field during chronological aging could induce genomic DNA damage
Published in International Journal of Environmental Health Research, 2022
Silvia Mercado-Sáenz, Beatriz López-Díaz, Antonio M. Burgos-Molina, Francisco Sendra-Portero, Alejandro González-Vidal, Miguel J. Ruiz-Gómez
The exposure to pulsed MF induces, within a cell, an electric field (E; in V/m) that depends on the radius of the yeast cell. Its value can be obtained from the magnetic flux density (B; in Tesla), its frequency (f; in Hz), and the cell radius (r; in meters) (Ruiz Gómez et al. 1999). As described in a previous work in the characterization of the pulsed MF (Ruiz-Gómez et al. 2002), in accordance with the Faraday’s Law of Induction and considering a circular contour parallel to the coils, also considering a homogeneous MF in the inner surface of the contour, the induced electromotive force (ξ) can be calculated and measured. At the low frequency used (25 Hz) the MF is proportional to the intensity of current that flows in the coils (Biot & Savart law). After the values of peak pulses (positive and negative) of ξ measurements, in an oscilloscope for pulsed MF, the corresponding peak values of E were obtained from the equation E = ξ/(2 π r). The measurements were performed using circular pickup coils in air of different radii (r = 2, r = 3 and r = 4 cm). The values calculated for E were E = 0.5, E = 0.7 and E = 0.8 V/m, respectively, for the positive pulses and E = 2.98, E = 3.82 and E = 3.98 V/m, respectively, for the negatives. After plotting the obtained values of E versus r for the pickup coils, a linear adjustment was made and the value of E for the mean radius of a yeast cell was extrapolated. Then, the electric current density (J; in A/m2) was calculated from the values of E and the cytoplasm conductivity (σ; in S/m) using the equation: J = σE. In addition, the value of Specific Absorption Rate (SAR; in W/kg) was obtained as SAR = (σE2)/d; being d = cytoplasm density, measured in Kg/m3.