Question

multiple choice 1 point
two oppositely - charged particles in a thundercloud are separated by 2.0 m. the force between them is measured as 9.0×10^(-6) n. using coulombs law, what is the magnitude of the charge on each particle (assume equal charge)? use this formula: f = k\frac{q^{2}}{r^{2}}, k = 8.99×10^{9}\frac{n·m^{2}}{c^{2}}
step 1: write the knowns
· force, f = 9.0×10^(-6) n
· distance, r = 2.0 m
· coulombs constant, k = 8.99×10^{9}\frac{n·m^{2}}{c^{2}}
· charges are equal: q1 = q2 = q
formula
f = k\frac{q^{2}}{r^{2}}
step 2: solve for q
6.3×10^(-10)c
1.0×10^(-4)c
6.3×10^(-8)c
2.0×10^(-4)c

Explanation:

Step1: Identify given values

$F = 9.0\times10^{-6}\ N$, $r = 2.0\ m$, $k=8.99\times 10^{9}\ \frac{N\cdot m^{2}}{C^{2}}$

Step2: Rearrange Coulomb's law formula for $q$

Starting with $F = k\frac{q^{2}}{r^{2}}$, we can solve for $q^{2}$ first: $q^{2}=\frac{F\cdot r^{2}}{k}$. Then $q=\sqrt{\frac{F\cdot r^{2}}{k}}$.

Step3: Substitute values and calculate

$q=\sqrt{\frac{9.0\times 10^{-6}\ N\times(2.0\ m)^{2}}{8.99\times 10^{9}\ \frac{N\cdot m^{2}}{C^{2}}}}=\sqrt{\frac{9.0\times 10^{-6}\times4.0}{8.99\times 10^{9}}}\ C\approx\sqrt{4.0\times 10^{-15}}\ C = 6.3\times 10^{-8}\ C$

Answer:

$6.3\times 10^{-8}\ C$ (corresponding to the correct option among the multiple - choice ones, which is the third option based on the visible options in the image)