Two point charges separated by a certain distance attract each other with an electric force of magnitude f_0f 0 . one charge is doubled while the other charge is left unchanged, and then the distance between the charges is tripled. what is the magnitude of the electric force between the charges in this new configuration (f_{\text{new}} =f new = ? )

F = 2/9* F₀

Explanation:

In the original situation, the force F₀ obeys the Coulomb's Law, so we can express F₀ as follows:

F₀ = k*q₁*q₂ / r₁₂² (1)

If we make q₂ₙ = 2*q₂, and r₁₂ₙ = 3*r₁₂, replacing in the Coulomb's Law expression, we have:

Fₙ = k*q₁*2*q₂ / (3*r₁₂)² = (2/9)*(k*q₁*q₂/r₁₂²) (2)

but (k*q₁*q₂/r₁₂²), from (1) ,is just F₀, so, replacing in (2), we have:

Fₙ = (2/9)*F₀

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