Question

Two charges are repelling each other with a force magnitude F. If each charge doubled and the distance between the charges became four times the original distance, determine the new magnitude of the force. (1/2)F 4F 2F 16 F (1/4)F

Answer 1

(1/4)F

Step-by-step explanation:

Let F be the force on charges q and q' separated by a distance, d

F = kqq'/d²

Now, if q and q' are doubled, our new charges are 2q and 2q' respectively and, if the distnace is increased by four times, then our new distance is 4d. So our new force F' = k (2q)(2q')/(4d)²

= 4kqq'/16d²

= kqq'/4d²

= F/4

So, the magnitude of our new force is F/4