Need help with linear approximation question

[John45]

alright so the question is

approximate the change in magnitude of the electrostatic force between two charges when the distance between them increase from r=20m to r =21m
F(r)= 0.01/(r^2)

I am uncertain of the answer or how to arrive to it
so if you can show me step by step that would be great

 

[tkhunny]

Have you met the first derivative?

\(\displaystyle dF = 0.01\cdot \frac{-2}{r^{3}}\;dr\)

r = 20 m
dr = 1 m

That's about it.

 

[John45]

ugh I tried taking the difference of both :|
thanks for the help but isn't magnitiude never negative?

 

[tkhunny]

You are not approximating "magnitude". You are approximating "change in magnitude".

Please do not try to tell me that things never shrink. :shock:

 

[Deleted member 4993]

alright so the question is

approximate the change in magnitude of the electrostatic force between two charges when the distance between them increase from r=20m to r =21m
F(r)= 0.01/(r^2)

I am uncertain of the answer or how to arrive to it
so if you can show me step by step that would be great

\(\displaystyle F(20) = \frac{0.01}{400}\)

\(\displaystyle F(21) = \frac{0.01}{441}\)

\(\displaystyle \delta F \ = \ |F(21) - F(20)|\)