Analytic calculations of the E-fields induced by time-varying magnetic fields generated by cylindrical gradient coils

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Abstract
Analytic expressions which allow the direct calculation of the electric field generated inside an infinite conducting cylinder by varying the current through the wires of any cylindrical coil are presented. These expressions provide some general insight into the spatial characteristics of the electric field generated inside the body by switched gradients and can be used to evaluate the locations where nerve stimulation by rapid gradient switching is likely to occur. They may also be employed at the design stage to produce gradient coils which can provide higher gradient switching rates without causing nerve stimulation. Using these expressions the electric field patterns produced by transverse and longitudinal, whole‐body gradient coils were calculated. Example data are presented along with the associated magnetic field patterns. The effect on the induced electric field pattern of varying the body size and the size of the region of gradient linearity was explored. Magn Reson Med 44:782–790, 2000.