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 fieldEzto the induced azimuthal fieldE&thgr;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 theEz/E&thgr;ratio to the design of coils and shields is discussed.