Question

Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10. (a) Is the new distance (1) less than 10, (2) equal to 10, or (3) greater than 10 times the original distance? Why?

Answer 1

New distance is less than 10.

Explanation:

The force acting between two charges is given by :

`F=k(q_1q_2)/(d^2)`

k is the electrostatic constant

d is the distance between charges

If two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10,
`F'=(F)/(10)`

New force is given by :

`F'=k(q_1q_2)/(d'^2)`

`(F)/(10)=k(q_1q_2)/(d'^2)`

`d'=√(10) * d`

So, the new distance is
`√(10)` times the original distance i.e. the new distance is less than 10 times the original distance. Hence, the correct option is (1).