The force between the two particles will quadruple
Explanation:
The magnitude of the electrostatic force between two charges is given by Coulomb's law:
[tex]F=k\frac{q_1 q_2}{d^2}[/tex]
where:
[tex]k=8.99\cdot 10^9 Nm^{-2}C^{-2}[/tex] is the Coulomb's constant
[tex]q_1, q_2[/tex] are the two charges
d is the separation between the two charges
In this problem, let's call F the initial force between the two charges, when they are at a distance of d.
Later, the distance between the two particles is halved, so the new distance is:
[tex]d'=\frac{d}{2}[/tex]
This means that the new electrostatic force will be:
[tex]F'=k\frac{q_1 q_2}{(d/2)^2}=4(k\frac{q_1 q_2}{d^2})=4F[/tex]
Therefore, the force between the two particles will quadruple.
Learn more about electrostatic force:
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