To determine the electric force between the two charged balloons, we can use Coulomb's law. Coulomb's law is given by the formula:
[tex]\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where:
- [tex]\( F \)[/tex] is the electric force between the charges,
- [tex]\( k \)[/tex] is Coulomb's constant, [tex]\( 9.0 \times 10^9 \, \text{newton-meter}^2 \text{coulomb}^{-2} \)[/tex],
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the charges on the balloons,
- [tex]\( r \)[/tex] is the distance between the charges.
Given:
- [tex]\( q_1 = 4.0 \times 10^{-6} \)[/tex] coulombs,
- [tex]\( q_2 = 8.2 \times 10^{-6} \)[/tex] coulombs,
- [tex]\( r = 2.0 \)[/tex] meters.
Let's substitute these values into Coulomb's law formula step-by-step to find the electric force:
1. Calculate the product of the charges:
[tex]\[ q_1 \cdot q_2 = (4.0 \times 10^{-6}) \cdot (8.2 \times 10^{-6}) \][/tex]
[tex]\[ = 32.8 \times 10^{-12} \, \text{coulombs}^2 \][/tex]
2. Calculate the square of the distance between the charges:
[tex]\[ r^2 = (2.0)^2 = 4.0 \, \text{meters}^2 \][/tex]
3. Now, apply Coulomb's law:
[tex]\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
[tex]\[ F = 9.0 \times 10^9 \cdot \frac{32.8 \times 10^{-12}}{4.0} \][/tex]
4. Simplify the expression:
[tex]\[ F = 9.0 \times 10^9 \cdot 8.2 \times 10^{-12} \][/tex]
5. Multiply the constants:
[tex]\[ F = 73.8 \times 10^{-3} \, \text{newtons} \][/tex]
6. Convert the result to a simpler notation:
[tex]\[ F = 0.0738 \, \text{newtons} \][/tex]
Thus, the electric force between the two balloons is [tex]\( 0.0738 \)[/tex] newtons. Therefore, the correct answer is:
C. [tex]\( 7.3 \times 10^{-2} \)[/tex] newtons
