How to use Coulomb's Law and proportionality to solve a question?

Question

Coulomb's Law: If two charges are 25cm apart, at what separation would the force between them be doubled and halved? I understand how to solve this by working with the whole formula, however can somebody show me how to do it using the inverse proportionally?

Basically, in the formula F = kq1q2 /r^2

What happens when to the distance r^2 when the force is 2F?

Please explain how to solve it using F directly proportional to 1/r^2 I know how to solve it by using the formula but not this way.. (using proportionality)

Answer 1

F = K / r^2 K = k q1 q2

What is the separation r for F to be halved ?

F1= K / (r1)^2

F2 = 1/2 F1 = K / (r2)^2

So ....

F2 / F1 = [ 1 / (r2)^2 ] / [ 1 / (r1)^2 ] = (r1)^2 / (r2)^2 = ( r1/r2 )^2

If F2 / F1 = 1/2 then

1/2 = ( r1/r2 )^2 ==> r1 / r2 = 0.707 ==> r2 = 1.414 r1

To find r2 for F being doubled, just let F2 / F1 = 2 and solve similarly

Answer 2

The Coulomb Force is inversely proportional to the square of the distance.

This can be written a F = k / r² , where k is a constant. If r is doubled, we can see that the value of F will decrease by a a factor of 4. Perhaps it is easiest to visualize if you start with r = 1.