The force will be reduced to 1/4 of the original
Explanation:
According to Coulomb's law, the force between two charges [tex]q_a\:\text{and}\:q_b,[/tex] separated by a distance r is given by
[tex]F = k\dfrac{q_aq_b}{r^2}[/tex]
where k is the Coulomb constant.
Now let F' be the force between the two charges when their separation distance is doubled. We can write this force as
[tex]F' = k\dfrac{q_aq_b}{(2r)^2} = k\dfrac{q_aq_b}{4r^2}[/tex]
[tex]\;\;\;\;\;= \frac{1}{4}\left(k\dfrac{q_aq_b}{r^2}\right) = \frac{1}{4}F[/tex]
Therefore, the force will be reduced to a quarter of its original value.
