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xvudi
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Homework Statement
I'm examining the equation Ohm_Max + dOhm/dr = Ohm_Max - dOhm/dr and can't find any solutions other than the trivial one, Ohm(r) = 0 for all r.
It's meant to determine if it is possible to build a length of conductor such that, upon dividing it at any arbitrary point, you'll find that the resistance behind is the same as the resistance ahead.
The Attempt at a Solution
Ohm(r) = 0. You can't have one because if Ohm(r) is even then dOhm/dr is odd.
Ohm(r) = Ohm_Max at r = 0 for bounds -L/2 to L/2, captured in the use of Ohm_Max the constant.
So the integral from -L/2 to 0 must equal the integral from 0 to L/2 meaning that dOhm/dr has to be even. This can't be as if Ohm(r) is odd then Ohm(0) must be 0 and not Ohm_Max. Odd functions cannot be valued at 0.
Now, mathematically why can't this work? I apologize for the absence of TeX. I'm still getting used to the forum interface.