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Simple differential calculus question with Force formula

Discussion in 'Mathematics and Physics' started by ElectroNewby, Aug 31, 2014.

  1. ElectroNewby

    ElectroNewby Member

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    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 !!
     
  2. MrAl

    MrAl Well-Known Member Most Helpful Member

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    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.
     
  3. ElectroNewby

    ElectroNewby Member

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

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