The new force between the charges when the distance become 2d will be F'=4F
When two charged particles are separated by the distance d then the force of attraction or repultion acts on the charged particle depending upon the nature of the charge whether it is positive or negative.
The formula for the electrostatic force is given by
[tex]F=\dfrac{kq_1q_2}{d^2}[/tex]
Now if the value of d becomes 2d then the formula will become:
[tex]F'=\dfrac{kq_1q_2}{(2d)^2}=\dfrac{kq_1q_2}{4d}[/tex]
[tex]\dfrac{F'}{F}=\dfrac{1}{4}[/tex]
[tex]F=4F'[/tex]
Hence the new force between the charges when the distance become 2d will be F'=4F
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