A little-known result of Townsend and Donaldson is extended to show that, for a solenoid carrying ac or rf current, the ratio of the average applied longitudinal field Ez to the induced azimuthal field Eθ at the periphery of the solenoid is equal to the ratio of the circumference of the solenoid to its pitch. For conventional solenoidal coils such as are used to excite electrodeless rf discharges, this ratio is typically ≳15–30. Applicability of the Ez/Eθ ratio to the design of coils and shields is discussed.
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Contaxes et al. (1969) studied this question.
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