Question

two equal charges, X distance apart exert force on one another the charge on one of the charges is doubled what is the ratio of distance between the two charges now and earlier if the force remains same in the two cases.

Answer 1

F=kq1q2/r^2
For 1st condition both the charges are equal q1=q2
so,
F=kq^2/r^2
r1^2=kq^2/F

Now if the charge is doubled

r2^2=kq(2q)/F

Ratio of the distances
r1^2/r2^2=kq^2/F×F/kq(2q)
r1/r2=underroot kq^2/F×F/kq(2q)
r1/r2=underroot q^2/2q^2
r1/r2=underroot 1/2


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