I need help with this question

Question

Two charged spheres are a fixed distance apart. If the charge on one sphere is decreased from 9 coulombs to 3 coulombs, the force it exerts on the other sphere becomes how many times weaker?

please write the formula properly, instead of F2 make it F_2.

_{Thank you!!}

Answer 1

Spheres of charge act the same way as point charges when you're not inside of them, so we can rephrase the question as "Two point charges are a fixed distance apart. If the charge on one point charge is decreased from 9 coulombs to 3 coulombs, the force it exerts on the other point charge becomes how many times weaker?

This inspires us to check out Colomb's law, the force between two charges:

F=K q₁q₂/r²

Where q₁ and q₂ are the two charges, and r is the distance between them. Let's suppose that q₁ is the one that changes from 9 to 3 coulombs (It doesn't matter which we pick, because we're multiplying the charges together, and the order we multiply numbers doesn't matter). This is the same effect as multiplying q₁ by 1/3. Since the force depends on q₁ directly (i.e. it's in the numerator and has no exponents), this will have the effect of multiplying the force by 1/3 as well, i.e. the force will be 1/3 as strong.