Answer:
Because the force is inversely proportional to the square of the distance
Explanation:
The magnitude of the electrostatic force between two charged particles is given by
[tex]F=k\frac{q_1 q_2}{d^2}[/tex]
where
k is the Coulomb's constant
q1, q2 are the magnitudes of the two charges
d is the distance between the two charges
We observe that the magnitude of the force is inversely proportional to the square of the distance.
Therefore, when the distance changes to
[tex]d'=\frac{d}{\sqrt{2}}[/tex]
The force will double:
[tex]F'=k\frac{q_1 q_2}{(d/\sqrt{2})^2}=2(k\frac{q_1 q_2}{d^2})=2F[/tex]
