Question

Two point charges are seperated by a distance R in air repel each other by a force F.One of the charges is doubled and the other is made one - fourth.For what new seperation between them will the force remain same?

Answer 1

\[1/\sqrt{2}\]R
whre R is the distance between two charges in case one

Answer 2

\[F=KQ _{1} Q _{2}/R ^{2}\]
\[F´=K2Q _{1} Q _{2}/4R ´^{2}\]

FOR F=F´ THEN
\[KQ _{1} Q _{2}/R ^{2}=K2Q _{1} Q _{2}/4R´ ^{2}\]
\[1/R ^{2}=2/4R´ ^{2}\]
\[R´ ^{2}=R ^{2}/2\]
\[R´=R \sqrt{2}/2\]