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Nony

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The paper describes correction factors for doing 4 probe conductivity measurements on cylinders (semiconductor wafers, sintered ceramic specimens, etc.). Intuitively, it makes sense to me that there would be these sorts of correction factors (paths of current flow are in parallel, but going deeper into the sample, would cover a longer distance, thus higher resistance). I have used the paper routinely, but IANAP and I never verified the paper itself--just plug and chugged the factors from the table.

1. Was wondering, for those who are physicists how "hard" is this as a problem (to do the method of images and create the table of correction factors for geometry)? Is it a routine HW problem in undergrad or graduate E&M? If so what text (edition and page #)? If not, I would think it would be nice HW problem because it actually is a practical result and kind of an intuitive geometry. If too easy for grad E&M than junior year E&M? It definitely feels harder than intro physics, which is the only course I have taken.

2. Also, I don't know if this has been done yet, but some extension of the paper would be useful:

A. Slight deviations from centerline (in and perpendicular to the 4 points line) of pellet. How much does the true answer change, based on using the assumption that we are centered? Note, that there are no correction factors for this since you sort of "by eye" center the sample. [I guess if you had an industrial, repeating process, you could build a jig, but this is not the normal instrument.]

B. How much will warping of the pellet affect the true answer versus measured? [Uniaxially pressed ceramic pellets usually have a slight but visible warping from strains created in the specimen during compaction prior to heating.]

[It might be more "easy" classical physics calculation, but would still be very nice for people who just use the instrument and want more corrections! (The people who make new material samples are not the type to derive E&M correction factors.) Even if you think the result is trivial, could be more HW problems for the courses.]