Answer :
ANSWER:
18 N
STEP-BY-STEP EXPLANATION:
Force between two charge particles is given by:
[tex]F=k\frac{q_1\cdot q_2}{d^2}[/tex]We can make the following relationship:
[tex]\begin{gathered} F_1=k\frac{q_1\cdot q_2}{d_1^2} \\ \\ F_2=k\frac{q_1\cdot q_2}{d_2^2} \\ \\ \frac{F_2}{F_1}=\frac{k\frac{q_1\cdot q_2}{d_2^2}}{k\frac{q_1\cdot q_2}{d_1^2}} \\ \\ \frac{F_2}{F_1}=\frac{d_2^2}{d_1^2} \\ \\ \frac{F_{2}}{F_{1}}=\left(\frac{d_1}{d_2}\right)^2 \end{gathered}[/tex]Therefore, we can establish the following:
[tex]\begin{gathered} \frac{F_2}{F_1}=\left(\frac{d_1}{d_2}\right)^2 \\ \\ \text{ We replacing:} \\ \\ \frac{F_2}{2}=\left(\frac{1}{\frac{1}{3}}\right)^2 \\ \\ F_2=2\cdot9 \\ \\ F_2=18\text{ N} \end{gathered}[/tex]Therefore, the force will now be 18 N at each charge.