Question

If the distance between two charges is increased to three times the original distance, how will the electrical force between the charges compare with the original force?it will increase to three times the original force.it will increase to nine times the original force.it will decrease to one-third the original force.it will decrease to one-ninth the original force.

Answer 1

The electrical force between two charges is given by
$F=k \frac{q_1 q_2}{r^2}$
where
k is the Coulomb's constant
q1 and q2 are the two charges
r is the distance between the two charges

We see that the magnitude of the force is inversely proportional to the square of the distance. Therefore, if the distance is increased to 3 times the original distance:
$r'=3 r$
the magnitude of the force will change as
$F' \sim \frac{1}{(3r)^2}= \frac{1}{9 r^2} = \frac{1}{9} F$

So, the correct answer is it will decrease to one-ninth the original force.