Faraday cage profiles giving self-similar charge drift and conduction in insulator samples

The well-known Faraday cage method for measuring drift and conduction of charges on the surface and inside insulators, consists of enclosing the charged specimen in an insulated metal cage, and measuring the current induced to the cage as the charge leaks away from the specimen into its grounded supports. However, for Faraday cages shaped for workshop convenience, it has proven very difficult to analyze the measured current decay curves to get the desired information about drift and conduction mechanisms. The present work employs a different strategy, namely to find Faraday cage shapes that lead to self-similar charge decay and simple, analytical formulas for the current decay in terms of charge mobility and conduction. For plane film specimens these shapes are hyperboloids, with a 90° corner as simple and very practical limit. In the axially symmetric cylindrical case, the sample is a straight cylinder, the cage profile follows a formula derived in the present work, and end effects are avoided