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?

Question

anonymous · Answer

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

anonymous · Answer

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