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What is the electric force acting between two charges of [tex]-0.0050 \, C[/tex] and [tex]0.0050 \, C[/tex] that are [tex]0.025 \, m[/tex] apart?

Use [tex]F = \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]-3.6 \times 10^8 \, N[/tex]

B. [tex]3.6 \times 10^8 \, N[/tex]

C. [tex]-9.0 \times 10^6 \, N[/tex]

D. [tex]9.0 \times 10^6 \, 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:
- Charge [tex]\( q_1 = -0.0050 \)[/tex] Coulombs (C)
- Charge [tex]\( q_2 = 0.0050 \)[/tex] Coulombs (C)
- Distance [tex]\( r = 0.025 \)[/tex] meters (m)
- Coulomb's constant [tex]\( k = 9.00 \times 10^9 \)[/tex] Newton meter squared per Coulomb squared (N·m²/C²)

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

3. Substitute the given values into the formula:
[tex]\[ F = \frac{(9.00 \times 10^9) \times (-0.0050) \times (0.0050)}{(0.025)^2} \][/tex]

4. Calculate the denominator:
[tex]\[ (0.025)^2 = 0.000625 \][/tex]

5. Calculate the numerator:
[tex]\[ (9.00 \times 10^9) \times (-0.0050) \times (0.0050) = (9.00 \times 10^9) \times (-0.000025) = -225000000.0 \][/tex]

6. Divide the numerator by the denominator:
[tex]\[ F = \frac{-225000000.0}{0.000625} = -360000000.0 \text{ N} \][/tex]

7. Take the magnitude for the final choice selections:
The magnitude of the force is:
[tex]\[ |F| = 360000000.0 \text{ N} \][/tex]

Thus, the correct magnitude answer is:
[tex]\[ \boxed{3.6 \times 10^8 \text{ N}} \][/tex]

Let's match this with the given choices:
A. [tex]\(-3.6 \times 10^8 \text{ N}\)[/tex]
B. [tex]\(3.6 \times 10^8 \text{ N}\)[/tex]
C. [tex]\(-9.0 \times 10^6 \text{ N}\)[/tex]
D. [tex]\(9.0 \times 10^6 \text{ N}\)[/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{B. \ 3.6 \times 10^8 \text{ N}} \][/tex]

This solution comprehends both the magnitude and the options given, but ensuring the final answer format adheres to positive magnitude considering the options provided.
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