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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 11, Iss. 4 — Oct. 1, 1925
  • pp: 375–391

THE THEORY OF THE SINGLE FIBER ELECTROSCOPE AND A NEW DESIGN OF THE INSTRUMENT

W. F. G. SWANN

JOSA, Vol. 11, Issue 4, pp. 375-391 (1925)
http://dx.doi.org/10.1364/JOSA.11.000375


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Abstract

If k is the mechanical restoring force per unit displacement of the fiber, the actual restoring force per unit displacement may readily be shown to be k-CX2, where C is the capacity of the fiber and X the field between the plates. The deflecting force due to a change of potential δV in the fiber is CXδV, so that the sensitivity S is S=CX/(k-CX2). If k is less than CX2 the instrument is unstable, and the fiber flies to either one plate or the other. The sensitivity becomes very large if k-CX2 is small; and in obtaining high sensitivity from the instrument, this condition is usually satisfied, even though the fact may not be realized. It is a bad condition since it results in large variations in S for small variations in either k or X. If we desire to restrict ourselves to the case k-CX2=k/2, so that we draw upon the term CX2 to the extent of no more than doubling the sensitivity which we should obtain in its absence, S reduces to the very simple expression S=1/X which, under a magnification of 100, gives a deflection of 1000 mm per volt for a field of one volt per cm between the plates. High sensitivity consistent with great constancy necessitates a small field between the plates and correspondingly small value of k. An instrument meeting the required conditions is described. As an illustration of the performance of the electroscope one experiment gave, with a magnification of 600, and a potential difference of 6 volts between plates, a sensitivity of 3500 eyepiece divisions per volt and a period so short that the fiber assumed a steady reading in less than ¾ second after application of the potential. Moreover, the linearity of the calibration curve over the whole range of the eyepiece scale was so perfect that departures from linearity could not be observed within the limits of accuracy of the readings.

Citation
W. F. G. SWANN, "THE THEORY OF THE SINGLE FIBER ELECTROSCOPE AND A NEW DESIGN OF THE INSTRUMENT," J. Opt. Soc. Am. 11, 375-391 (1925)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-11-4-375


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References

  1. The attraction of the fiber for its images in the plates is negligible, and is here neglected.
  2. A more rigorous presentation of the matter is the following. Suppose q11, q12, q13 are the coefficient of capacity of the fiber and its coefficients of induction in relation to the plates in the displaced position represented by δx. Then, if the fiber be displaced subject to the condition that its charge remains zero, its potential will change by Xδx and we shall have q12V2+q13V3+q11Xδx=0 where V2 and V3 refer to the potentials of the plates. If, keeping the fiber in the same position, it be brought to zero potential, and if Q is the charge which comes to it under these conditions q12V2+q13V3+q11×0=Q. Hence, from these two equations Q = -q11Xδx agreeing with the result in the text when C is written for q11. In practice it is, of course, sufficient to regard C as pertaining to the fiber for its undetected position.
  3. This value of the capacity may readily be obtained as a very close approximation in the case of infinite plates by considering the fiber and its various images in the plates and then paring them off suitably in such a way as to leave only the fiber itself and its image in one of the plates.
  4. Since this paper was written I have received, through the courtesy of Professor Siegbahn a publication "Undersökningar rörande Elektrometrar" by Gustaf Ising, published by Gleerupska Universitetsbokhandeln, Lund, in which an account is given of a single fiber electroscope of design somewhat different from that here described. The author also appears to go into the general theory of this and many other instruments. The publication had escaped me as it is not in one of the regular journals, but is printed separately as a Doctor's thesis, and is in Swedish.

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