Answer: 12 N
Explanation:
The electric force (F) between two charged objects is given by Coulomb's Law:
[tex]F = \dfrac{kqQ}{r^{2} }[/tex], where:
The force (F) is given as 3 N when the objects are 2 meters apart (r). Let's denote these initial values as F₁ = 3 and r₁ = 2.
[tex]F_{1} = \dfrac{kqQ}{r_{1} ^{2} }[/tex]
We want to find the force when the distance between them is 1 meter. Let's denote these values as F₂ and r₂ = 1.
[tex]F_{2} = \dfrac{kqQ}{r_{2} ^{2} }[/tex]
Since k, q, and Q remain constant, we can set up a ratio:
[tex]\dfrac{F_{2}}{F_{1}}= \dfrac{r_{1} ^{2} }{r_{2} ^{2} }[/tex]
Now, substitute the given values:
[tex]\dfrac{F_{2}}{3}}= \dfrac{2 ^{2} }{1 ^{2} }[/tex]
Solve for F₂:
F₂ = 3(4)
F₂ = 12 N
When the objects are brought closer together to 1 meter, the electric force between them becomes 12 N.
