How Does Changing Distance Affect Force Between Charges?

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SUMMARY

The discussion focuses on the relationship between distance and force between two point charges, specifically how to change the distance to alter the force by a factor of ten. The relevant equations are F1 = kq1/r1² and F2 = kq2/r2². The correct ratio of distances is derived as r1/r2 = √(F2/F1) = 1/√10, clarifying that F2 is on top of the fraction due to the nature of the force relationship. The confusion arises from incorrect initial equations, which were corrected by a participant in the forum.

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  • Understanding of Coulomb's Law
  • Familiarity with the concept of electric force
  • Basic algebra skills for manipulating equations
  • Knowledge of square root functions
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  • Learn about the implications of distance in electrostatic forces
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This discussion is beneficial for physics students, educators, and anyone seeking to understand the principles of electrostatics and the mathematical relationships governing electric forces.

dummie90
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Homework Statement


By what factor must you change the distance between two point charges to change the force between them by a factor of ten?


Homework Equations


F1=kq1/r^2
F2=kq2/r^2



The Attempt at a Solution


F1:F2= 10
r1/r2=sq.root(F2/F1)= 1/sqroot10

I do not understand how to get to r1/r2=sq.root(F2/F1)= 1/sqroot10
I do understand that you square root F2/F1 to get rid of the square of r. but why is F2 on top of the fraction instead of F1 (i.e. sqroot F1/F2) and how does that become 1/sqroot 10? And how did that equation even come about?

Sorry I'm very confused I've tried to make sense of this worked example many times,
Thank you so much for the help
 
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Welcome to PF!

dummie90 said:
F1=kq1/r^2
F2=kq2/r^2
…
Sorry I'm very confused …

Hi dummie90! Welcome to PF! :smile:

(have a square-root: √ :smile:)

You're very confused because your equations are wrong. :wink:

They should be:

F1=kqQ/r1^2
F2=kqQ/r2^2

now can you see how it comes out as √(F2/F1)? :smile:
 

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