From Columb's Law which describe the electrostatic interaction.
The formula is given and looks as follows \(F=k \frac{|q1*q2|}{r^{2} }\)
where:
F is force acting between charges,
q1 - charge one given in columbs,
q2 - charge two given in columbs,
r - distance between charge in meters
k - constant
First, we have to convert out formula to get r.
\(F=k \frac{q1*q2}{r^{2} }\)
Now we multiplaty by \(r^{2}\) both sides of equation
\(F* r^{2} =k*|q1*q2|\)
Now we devide both sides by F
\(r^{2} =k \frac{|q1*q2|}{F}\)
Next step is take square root
\(r= \sqrt{k \frac{|q1*q2|}{F}}\)
We have all date, we can subsitute it to our formula
\(r= \sqrt{k* \frac{|q1q2"}{F} } = \sqrt[2]{8.9* 10^{9* \frac{0.001*0.001}{200} }} = 6.67 [m]\)
