The electric force between two charged balloons is 0.16 newtons. If the distance between them is doubled, what will the new force between them be?
A. 0.04 newtons
B. 0.08 newtons
C. 0.32 newtons
D. 0.64 newtons
So we wan't to know what will the Coulomb force be between two charged baloons will be if we double the distance between the them and Fc=0.16N. The coulomb force between two charges is Fc=k*Q1*Q2/r^2. So we see from the equation that the magnitude of the force will be smaller as we increase the distance. So let's increase the distance from r to R=2r. If we input thai into the equation we get: Fc=k*Q1*Q2/R^2. Now: Fc=k*Q1*Q2/(2r)^2. And finally: Fc= k*Q1*Q2/4r^2. And if we factor out 1/4 we get: Fc=(1/4)*k*Q1*Q2/r^2. Now we can see that if we double the distance the magnitude of the force will be smaller for a factor of 1/4 or the magnitude of the force will be smaller 4 times. So finally the force is (1/4)*0.16N= 0.04N. So the correct answer is A. 0.04 newtons.
