Two charged spheres are 16 cm apart. If the spheres are moved closer to
each other so that they are 8 cm apart, how will the force between them
change? *
The force will decrease by a factor of 2
O
The force will increase by a factor of 2
The force will decrease by a factor of 4
The force will increase by a factor of 4

Correct  Fourth statement is true - the force will increase by a factor of 4

Explanation:

The formula for calculating the Coulomb force between two charged objects, in this case spheres is:

Fc = k · q₁ · q₂ / r² Coulomb force

Given:

r₁ = 16 cm initial distance between spheres

r₂ = 8 cm final distance between spheres

The Coulomb force for initial distance is:

Fc₁ = k · q₁ · q₂ / r₁²

The Coulomb force for final distance is:

Fc₂ = k · q₁ · q₂ / r₂²

their relationship is:

Fc₂ / Fc₁ = (k · q₁ · q₂ / r₂²) / (k · q₁ · q₂ / r₁²)  this is a double fraction

Fc₂ / Fc₁ = (k · q₁ · q₂ · r₁²) / (k · q₁ · q₂ · r₂²)

when we shorten the same value we get:

Fc₂ / Fc₁ =  r₁² / r₂² = 16² / 8² =  (16 / 8) ² = 2² = 4

Fc₂ / Fc₁ = 4  ⇒ Fc₂ = 4 · Fc₁

Which meaning that the force will increase by a factor of 4

God is with you!!!

real, smaller and upside-down.   so the answer should be b.