Does anyone else get as confused as I do with negative signs when trying to
derive the potential for a point charge?
I finally figured out my confusion but the process of :
1) delta PE = (negative) of Work done by the field
2) so that F = -qE
3) so that delta V = - integral (E dot ds)
4) BUT now dr = -ds (this is what took me a while to see)
5) so that delta V = - integral (Edr)
6) which is (for point charge) deltaV = - integral (kQ/r^2) dr
7) which integral generates another negative so delta V = kQ/r
That dr = -ds is always my stumbling block because most texts don't really
spell it out. HR&K just jump from E dot ds to Edr.
Anyway--just venting and acknowledging that this HAS to be confusing to
students who are just coming off of Gauss' Law which always confuses the
hell out of them--for reasons I don't quite understand!
Rick
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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
rtarara@saintmarys.edu
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