Force F acts between two charges, q1 and q2, separated by a distance d. If q1 is increased to twice its original value and the distance between the charges is also doubled, what is the new force acting between the charges in terms of F? F F F 2F
Okay, haven't done physics in years, let's see if I remember this.
So Coulomb's Law states that [tex]F = k \frac{Q_1Q_2}{d^2}[/tex] so if we double the charge on [tex]Q_1[/tex] and double the distance to [tex](2d)[/tex] we plug these into the equation to find
[tex]F_{new} = k \frac{2Q_1Q_2}{(2d)^2}=k \frac{2Q_1Q_2}{4d^2} = \frac{2}{4} \cdot k \frac{Q_1Q_2}{d^2} = \frac{1}{2} \cdot F_{old}[/tex]
So we see the new force is exactly 1/2 of the old force so your answer should be [tex]\frac{1}{2}F[/tex] if I can remember my physics correctly.
