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On the supplemental problems for pset 8, question 4A-4, it says the force field has a magnitude of k/r. The "expression" for this force field has the scalar multiplier k/r^2. I don't understand the reasoning for r to become r^2 when k stays the same.

OCW Scholar - Multivariable Calculus
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<-y,x> has a magnitude of: \[y ^{2}+x ^{2}.\] And that magnitude is an equation for a circle. So we can represent that magnitude by \[r ^{2}.\] In order to scale that magnitude to the required magnitude of:\[\frac{ 1 }{ r },\] we need to multiply the vector <-y,x> by \[\frac{ 1 }{ r ^{2} }.\]

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