1.
[tex]Dane:\\q_1 = 5 \ \mu C = 5\cdot10^{-6} \ C\\q_2 = 2 \ \mu C = 2\cdot10^{-6} \ C\\F = 50 \ nN = 50\cdot10^{-9} \ N\\k = 9\cdot10^{9}\frac{Nm^{2}}{C^{2}}\\Szukane:\\r = ?\\\\\\F = k\cdot\frac{q_1\cdot q_2}{r^{2}} \ \ /\cdot r^{2}\\\\F\cdot r^{2} = k\cdot q_1\cdot q_2 \ \ /:F\\\\r^{2} = \frac{k\cdod q_1q_2}{F}\\\\r = \sqrt{\frac{k\cdot q_1q_2}{F}}\\\\r = \sqrt{\frac{9\cdot10^{9}\frac{Nm^{2}}{C^{2}}\cdot5\cdot10^{-6} \ C\cdot 2\cdot10^{-6} \ C}{50\cdot10^{-9} \ N}}\\\\r = \sqrt{1,8\cdot10^{6} \ m^{2}}[/tex]
[tex]\boxed{r = 1,342\cdot10^{3} \ m = 1 \ 342 \ m}[/tex]
2.
[tex]Dane:\\q_1 = 3 \ \mu C = 3\cdot10^{-6} \ C\\q_2 = 4 \ \mu C = 4\cdot10^{-6} \ C\\F = 90 \ nN = 90\cdot10^{-9} \ N\\k = 9\cdot10^{9}\frac{Nm^{2}}{C^{2}}\\Szukane:\\r = ?\\\\\\F = k\cdot\frac{q_1q_2}{r^{2}} \ \ /\cdot r^{2}\\\\F\cdot r^{2} = k\cdot q_1q_2 \ \ /:F\\\\r^{2} = \frac{k\cdot q_1q_2}{F}\\\\r = \sqrt{\frac{k\cdot q_1q_2}{F}}\\\\r = \sqrt{\frac{9\cdot10^{9}\frac{Nm^{2}}{C^{2}}\cdot3\cdot10^{-6} \ C \cdot4\cdot10^{-6} \ C}{90\cdot10^{-9} \ N}[/tex]
[tex]r = \sqrt{1,2\cdot10^{6} \ m^{2}}\\\\\boxed{r = 1,095\cdot10^{3} \ m = 1 \ 095 \ m}[/tex]
