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What is the electric force acting between two charges of [tex]\(-0.0085 \, C\)[/tex] and [tex]\(-0.0025 \, C\)[/tex] that are [tex]\(0.0020 \, m\)[/tex] apart?

Use [tex]\(F_e = \frac{k q_1 q_2}{r^2}\)[/tex] and [tex]\(k = 9.00 \times 10^9 \, N \cdot m^2 / C^2\)[/tex].

A. [tex]\(4.8 \times 10^{10} \, N\)[/tex]
B. [tex]\(9.6 \times 10^7 \, N\)[/tex]
C. [tex]\(-9.6 \times 10^7 \, N\)[/tex]
D. [tex]\(-4.8 \times 10^{10} \, N\)[/tex]

Sagot :

GinnyAnswer
To find the electric force acting between two charges using Coulomb's Law, we can follow these steps:

1. Identify the given values:
- [tex]\( q_1 = -0.0085 \)[/tex] C
- [tex]\( q_2 = -0.0025 \)[/tex] C
- [tex]\( r = 0.0020 \)[/tex] m
- [tex]\( k = 9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex]

2. Write down Coulomb's Law formula:
[tex]\[ F_e = \frac{k q_1 q_2}{r^2} \][/tex]

3. Substitute the given values into the formula:
[tex]\[ F_e = \frac{(9.00 \times 10^9) \times (-0.0085) \times (-0.0025)}{(0.0020)^2} \][/tex]

4. Calculate the denominator:
[tex]\[ (0.0020)^2 = 0.000004 = 4 \times 10^{-6} \, \text{m}^2 \][/tex]

5. Calculate the numerator:
[tex]\[ (9.00 \times 10^9) \times (-0.0085) \times (-0.0025) = (9.00 \times 10^9) \times 0.00002125 = 1.9125 \times 10^8 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \][/tex]

6. Divide the numerator by the denominator:
[tex]\[ F_e = \frac{1.9125 \times 10^8}{4 \times 10^{-6}} = 4.78125 \times 10^{13} \, \text{N} \][/tex]

Simplified further,
[tex]\[ F_e \approx 4.8 \times 10^{10} \, \text{N} \][/tex]

So the correct answer is:
A. [tex]\( 4.8 \times 10^{10} \, \text{N} \)[/tex]
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