Answer: 1.51 km
Explanation:
Coulomb's Law: The electrostatic force between two charge particles Q: and Q2 is directly proportional to product of magnitude of charges and inversely proportional to square of separation distance between them.
Or, [tex]\vec{F}=k \frac{Q_{1} Q_{2}}{r^{2}}[/tex]
Where Q1 and Q2 are magnitude of two charges and r is distance between them:
Given:
Q1 = Charge near top of cloud = 48.8 C
Q2 = Charge near the bottom of cloud = -41.7 C
Force between charge at top and bottom of cloud (i.e. between Q: and Q2) (F) = 7.98 x 10^6N
k = 8.99 x 109Nm^2/C^2
So,
[tex]\begin{aligned}&7.98 \times 10^{6}=\left(8.99 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right) \frac{48.8 \mathrm{C} \times 41.7 \mathrm{C}}{\mathrm{r}^{2}} \\&r=\sqrt{\frac{1.8294 \times 10^{13}}{7.98 \times 10^{6}}}=1.514 \times 10^{3} \mathrm{~m}=1.51 \mathrm{~km}\end{aligned}[/tex]
Therefore, the separation between the two charges (r) = 1.51 km
