Simple differential calculus question with Force formula

[ElectroNewby]

Hi
I'm starting calculus and so far so good (doing the slopes)

But I'm having a hard time figuring how to find my f(y1), f(y2) in this formula: ||F|| = ([(9 × 10⁹) ((N × m²) / C²)] Q1Q2) / r²

Q1 = 5 µC
Q2 = 10 µC

I need to find the "mean variation rate" (or whatever you call it in English, sorry ?) of the force intensity in regards to the distance if the distance between the two charges goes from 30 mm to 40 mm.

I know that it'll be Δ||F|| divided by Δr but I'm not able to process Δ||F||
I'm supposed to obtain -21.875N/mm

So basically, what do I replace the bold letters with in : ||F|| = ([(9 × 10⁹) ((N × m²) / C²)] Q1Q2) / r²

Thank you so much !!

 

[MrAl]

Hi,

To start, isnt the N*m^2/C^2 part just the *units* of the 9x10^9 factor (ie Coulombs constant)?

This makes it:
|F|=K*Q1*Q1/r^2
K being the aforementioned constant.
After that you should be able to use the mean value theorem.

 

[ElectroNewby]

As always, thank you so much ! This was quite an hassle for nothing, and was easily resolved with your solution