Charge Growth Equation for Belts of Insulating Materials Passing over Grounded Rollers

Abstract
The magnitude of the electrostatic charge density on an insulating belt of photographic film increases as the belt passes repeatedly over a set of grounded metal rollers. The charge density q asymptotically approaches an equilibrium value qe according to the relation q = qe (1 − e−n/τ), where n is the number of roller passages and τ is an arbitrary constant. An equivalent circuit which describes this behavior is presented. The circuit elements are an electromotive force, a contact resistance, a leakage resistance, and a capacitance between the belt and the roller. The physical equivalents of these elements and the possibility of their measurement are discussed.

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