How Does Changing Distance Affect Force Between Charges?

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To change the force between two point charges by a factor of ten, the distance must be adjusted according to the inverse square law of electrostatic force. The correct relationship is derived from the equations F1 = kq1/r1^2 and F2 = kq2/r2^2. The confusion arises from the application of the square root in the ratio of forces, where F2 is placed over F1 to maintain the correct relationship. The result shows that the ratio of distances, r1/r2, equals 1/sqrt(10) when the force changes by a factor of ten. Understanding this relationship clarifies how distance affects the force between charges.
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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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