We know that F varies jointly with q1 and q2 and inversely as the square of d, that means that we can write it as:
[tex]F=k\frac{q_1q_2}{d^2}[/tex]where k is a constant. To find k we plug the values given and solve the equation:
[tex]\begin{gathered} 80=k\frac{4\cdot16}{0.4^2} \\ 80=k\frac{64}{0.16} \\ 80=400k \\ k=\frac{80}{400} \\ k=\frac{1}{5} \end{gathered}[/tex]Hence the expression for F is:
[tex]F=\frac{q_1q_2}{5d^2}[/tex]Now, plugging the values given we have:
[tex]\begin{gathered} F=\frac{(12)(20)}{5(0.2)^2} \\ F=1200 \end{gathered}[/tex]Therefore F=1200.
