The method of images is applied to find the net resistance of a square lamina whose input/output currents are through point contacts at opposite corners. This application illustrates the rare use of the method of images with an infinite number of image charges.
REFERENCES
1.
Theodore F.
Bogert
, Jr., Electric Circuits
, 2nd ed. (McGraw-Hill
, Westerville, OH
, 1998
).2.
David J.
Griffiths
, Introduction to Electrodynamics
, 2nd ed. (Prentice Hall
, Englewood Cliffs, NJ
, 1989
).3.
An infinite line of image point charges can aid in finding the potential between two parallel plates containing a point charge. See for example
Jon
Pumplin
, “Application of Sommerfeld-Watson transformation to an electrostatics problem
,” Am. J. Phys.
37
, 737
–739
(1969
).4.
The author is indebted to an anonymous referee for pointing out this example:
W. R.
Smythe
, Static and Dynamic Electricity
(McGraw-Hill
, New York
, 1968
), pp. 118
–121
.5.
L. J.
Van der Pauw
, “A method of measuring specific resistivity and Hall effect of discs of arbitrary shape
,” Philips Res. Rep.
13
, 1
–9
(1958
).6.
The literature on the measurement of resistance of thin films is legion. An excellent summary of applications of the four-point measurement technique and its theoretical basis can be found at
⟨www.sjsu.edu/faculty/selvaduray/page/papers/mate210/thinfilm.pdf⟩.© 2009 American Association of Physics Teachers.
2009
American Association of Physics Teachers
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