Let's solve this problem step-by-step.
We're given the following data:
1. Charge [tex]\( q_1 = 6.33 \mu C \)[/tex]
2. Force [tex]\( F = 0.115 \, N \)[/tex]
3. Distance [tex]\( r = 1.44 \, m \)[/tex]
4. Coulomb's constant [tex]\( k = 8.99 \times 10^9 \, N \, m^2 / C^2 \)[/tex]
The goal is to find the value of the second charge [tex]\( q_2 \)[/tex].
1. Convert the given charge [tex]\( q_1 \)[/tex] from microcoulombs to coulombs:
[tex]\[ q_1 = 6.33 \, \mu C \times 10^{-6} = 6.33 \times 10^{-6} \, C \][/tex]
2. Use Coulomb's Law:
[tex]\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
We need to solve for [tex]\( q_2 \)[/tex]:
[tex]\[ q_2 = \frac{F \cdot r^2}{k \cdot q_1} \][/tex]
3. Substitute the given values into the equation:
[tex]\[ q_2 = \frac{0.115 \, N \cdot (1.44 \, m)^2}{(8.99 \times 10^9 \, N \, m^2 / C^2) \cdot (6.33 \times 10^{-6} \, C)} \][/tex]
4. Calculate [tex]\( q_2 \)[/tex]:
[tex]\[ q_2 = \frac{0.115 \cdot 2.0736}{8.99 \times 10^9 \cdot 6.33 \times 10^{-6}} \][/tex]
[tex]\[ q_2 \approx \frac{0.238464}{56.967 \times 10^3} \][/tex]
[tex]\[ q_2 \approx 4.190438032779971 \times 10^{-6} \, C \][/tex]
5. Convert the result back to microcoulombs:
[tex]\[ q_2 \approx 4.190438032779971 \, \mu C \][/tex]
### Conclusion
The value of the second charge [tex]\( q_2 \)[/tex] is approximately [tex]\( 4.19 \, \mu C \)[/tex]. Since it is attracting the positive charge [tex]\( q_1 \)[/tex], [tex]\( q_2 \)[/tex] must be a negative charge. Therefore, [tex]\( q_2 \approx -4.19 \, \mu C \)[/tex].
