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If the distance between the two equal po...

If the distance between the two equal point charges is doubled and their individual charges are doubled, what would happen to the force between them ?

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Let F be the force between the two equal point charges `q_1 and q_2` separated by distance r.
`F=1/(4piin_0)(q_1q_2)/(r^2)=1/(4piin_0)q^2/r^2`
`[:. q_1=q_2=q` (say)]
According to question
`q._(1) =q._(2)=2q and r. = 2r`
Now `F.=1/(4piin_0)(q._1q._2)/((r.)^2)`
`F.=1/(4piin_0)((2q)(2q))/((2r)^2)`
`F. = 1/(4piin_0) ((q^2))/((r^2))=F`
So the force remains same on doubling the charges and also the distance between them.
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