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Two balloons, one with a charge of [tex]$4.0 \times 10^{-6}$[/tex] coulombs and the other with a charge of [tex]$8.2 \times 10^{-6}$[/tex] coulombs, are kept 2.0 meters apart. What is the electric force between the two balloons? [tex]\kappa = 9.0 \times 10^9 \ \text{N} \ \text{m}^2 \ \text{C}^{-2}[/tex]

A. [tex][tex]$4.0 \times 10^{-2}$[/tex][/tex] newtons

B. [tex]$5.2 \times 10^{-2}$[/tex] newtons

C. [tex]$7.3 \times 10^{-2}$[/tex] newtons

D. [tex][tex]$8.2 \times 10^{-6}$[/tex][/tex] newtons



Answer :

GinnyAnswer
To determine the electric force between two balloons with the given charges using Coulomb's law, we follow these steps:

1. Identify the charges and the distance between them:
- Charge 1 ([tex]\( q_1 \)[/tex]) is [tex]\(4.0 \times 10^{-6}\)[/tex] coulombs.
- Charge 2 ([tex]\( q_2 \)[/tex]) is [tex]\(8.2 \times 10^{-6}\)[/tex] coulombs.
- The distance ([tex]\( r \)[/tex]) between the charges is 2.0 meters.
- Coulomb's constant ([tex]\( k \)[/tex]) is [tex]\(9.0 \times 10^9 \)[/tex] N m²/C².

2. Write down Coulomb's law formula:
[tex]\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
where [tex]\( F \)[/tex] is the magnitude of the electric force between the two charges.

3. Substitute the given values into the formula:
[tex]\[ F = 9.0 \times 10^9 \frac{|4.0 \times 10^{-6} \cdot 8.2 \times 10^{-6}|}{2.0^2} \][/tex]

4. Calculate the product of the charges:
[tex]\[ q_1 \cdot q_2 = (4.0 \times 10^{-6}) \cdot (8.2 \times 10^{-6}) = 32.8 \times 10^{-12} \text{Coulomb}^2 \][/tex]

5. Compute the square of the distance:
[tex]\[ r^2 = (2.0)^2 = 4.0 \text{m}^2 \][/tex]

6. Substitute the values into the formula:
[tex]\[ F = 9.0 \times 10^9 \frac{32.8 \times 10^{-12}}{4.0} \][/tex]

7. Simplify the expression:
[tex]\[ F = 9.0 \times 10^9 \times 8.2 \times 10^{-12} \][/tex]

8. Perform the multiplication to find the force:
[tex]\[ F = 0.0738 \text{ newtons} \][/tex]

Therefore, the answer is:
c. [tex]\(7.3 \times 10^{-2}\)[/tex] newtons

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