0
RESEARCH PAPERS

An Electrooptic Analog for the Solution of the Laplace Equation

[+] Author and Article Information
R. O’Regan

Bell Telephone Laboratories, Inc., Murray Hill, N. J.

J. Appl. Mech 34(2), 452-456 (Jun 01, 1967) (5 pages) doi:10.1115/1.3607704 History: Received March 23, 1966; Revised August 10, 1966; Online September 14, 2011

Abstract

Laplace’s equation occurs frequently in mathematical physics for problems relating to fluid flow, heat transfer, and so on. For some simple cases, the boundary-value problem can be solved; but more often, the differential equation proves intractable, and numerical analysis or experimental methods are used. The electrooptic analog is an experimental method based upon the fact that an organic dye solution becomes birefringent in an electric field. This effect enables one to determine voltage gradient throughout a two-dimensional field. The boundary conditions most readily applied are prescribed constant values of the electric potential φ on conducting segments of a boundary and ∂φ/∂n = 0 on insulated segments of a boundary. With the known conditions on the boundary and the potential gradient found from experiment, the problem is solved. This analog can be used for all physical problems for which the boundary conditions are applicable, and which satisfy Laplace’s equation.

Copyright © 1967 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In