The original Coulomb force between the charges is:
Fc=(k*Q₁*Q₂)/r², where k is the Coulomb constant and k=9*10⁹ N m² C⁻², Q₁ is the first charge, Q₂ is the second charge and r is the distance between the charges.
The magnitude of the force is independent of the sign of the charge so I can simply say they are both positive.
Q₁ is decreased to Q₁₁=(1/3)*Q₁=Q₁/3 and
Q₂ is decreased to Q₂₂=(1/2)*Q₂=Q₂/2.
New force:
Fc₁=(k*Q₁₁*Q₂₂)r², now we input the decreased values of the charge
Fc₁=(k*{Q₁/3}*{Q₂/2})/r², that is equal to:
Fc₁=(k*(1/3)*(1/2)*Q₁*Q₂)/r²,
Fc₁=(k*(1/6)*Q₁*Q₂)/r²
Fc₁=(1/6)*(k*Q₁*Q₂)/r², and since the original force is: Fc=(k*Q₁*Q₂)/r² we get:
Fc₁=(1/6)*Fc
So the magnitude of the new force Fc₁ with decreased charges is 6 times smaller than the original force Fc.
