met4_5_S05 - INSTITUTE OF PHYSICS PUBLISHING Metrologia 41...

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I NSTITUTE OF PHYSICS PUBLISHING M ETROLOGIA Metrologia 41 (2004) S147–S158 PII: S0026-1394(04)80311-6 Automated electric charge measurements of Fuid microdrops using the Millikan method Eric R Lee, Valerie Halyo, Irwin T Lee and Martin L Perl Stanford Linear Accelerator Center, 2575 Sand Hill Road, Menlo Park, CA 94025, USA Received 23 January 2004 Published 16 September 2004 Online at doi:10.1088/0026-1394/41/5/S05 Abstract Automated measurements of the electric charge of ±uid microdrops precise to up to 0.016 of an electron charge have been made using machine-vision systems to observe the motion of ±uid microdrops in air under the in±uence of an oscillating electric ²eld. The ±uid drop diameters have ranged from 7 μm to 25 μm with smaller diameter drops being measured to higher precision. The experimental runs performed for the purpose of attempting to ²nd isolated fractionally electrically charged particles have measured the charges of tens of millions of ±uid microdrops using piezoelectrically driven drop-on-demand inkjet-like droplet ejectors as ±uid drop sources. 1. Introduction The quantization of free electric charge into units only of multiples of the unit charge on the electron and not into any smaller subfraction is an issue that is the subject historically of many experimental tests. One method of searching for isolated fractional electric charge has been to expand upon the method used by Robert Millikan to perform the original determination of the value of the fundamental unit charge by measuring the electric charges of ±uid microdrops based on their terminal velocities in a switched electric ²eld. The incorporation of machine-vision systems based on commercial grade CCD cameras coupled to personal computers, using microdrop generators based on inkjet printing technology has allowed automation of Millikan’s method using relatively low- cost hardware. The charge-measurement accuracy of these systems can be made limited only by the Brownian motion of the ±uid microdrops. 2. Measurement physics The principle behind the Millikan method of determining the electric charge on a ±uid microdrop of known speci²c gravity is to measure the terminal velocity of the microdrops under the in±uence of electric ²elds in a well-characterized gas environment and extract from these terminal velocity measurements the radius and the electric charge of the microdrops [1, 2]. The following quantities are used in this paper: F = force ρ = ±uid density m = microdrop mass g = gravitational acceleration v = drop velocity relative to air r = drop radius η = viscosity of air E = electric ²eld Q = charge on microdrop T = temperature k = Boltzmann’s constant t = time in seconds N e = Q/e number of electron charges 2.1. Stokes’ Law The charge on ±uid microdrops, using Millikan’s method, is determined by measuring the terminal velocity of the drop in a known electric ²eld. The drop is accelerated by the electric ²eld and reaches terminal velocity when the forces, due to
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This note was uploaded on 04/30/2008 for the course PHYSICS 2100 taught by Professor Livant during the Spring '08 term at Auburn University.

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met4_5_S05 - INSTITUTE OF PHYSICS PUBLISHING Metrologia 41...

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