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

Answer:

New distance is less than 10.

Explanation:

The force acting between two charges is given by :

$F=k\dfrac{q_1q_2}{d^2}$

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, $F'=\dfrac{F}{10}$  

New force is given by :

$F'=k\dfrac{q_1q_2}{d'^2}$

$\dfrac{F}{10}=k\dfrac{q_1q_2}{d'^2}$

$d'=\sqrt{10} \times d$

So, the new distance is $\sqrt{10}$ times the original distance i.e. the new distance is less than 10 times the original distance. Hence, the correct option is (1).