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 answer: 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!