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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_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]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]



Answer :

GinnyAnswer
To find the electric force acting between two charges using Coulomb's Law, we will use the formula:

[tex]\[ F_e = \frac{k \cdot q_1 \cdot q_2}{r^2} \][/tex]

where:
- [tex]\( q_1 = -0.0050 \, \text{C} \)[/tex]
- [tex]\( q_2 = 0.0050 \, \text{C} \)[/tex]
- [tex]\( r = 0.025 \, \text{m} \)[/tex]
- [tex]\( k = 9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \)[/tex]

Let's break this down step-by-step:

1. Substitute the values into the formula:

[tex]\[ F_e = \frac{(9.00 \times 10^9) \cdot (-0.0050) \cdot (0.0050)}{(0.025)^2} \][/tex]

2. Calculate the denominator [tex]\((r^2)\)[/tex]:

[tex]\[ (0.025)^2 = 0.000625 \, \text{m}^2\][/tex]

3. Calculate the numerator:

[tex]\[ (9.00 \times 10^9) \cdot (-0.0050) \cdot (0.0050) \][/tex]
[tex]\[ = (9.00 \times 10^9) \cdot (-0.000025) \][/tex]
[tex]\[ = -225 \times 10^3 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \][/tex]

4. Combine the numerator and the denominator:

[tex]\[ F_e = \frac{-225 \times 10^3}{0.000625} \][/tex]

5. Compute the division:

[tex]\[ F_e = -359999999.99999994 \, \text{N} \][/tex]
[tex]\[ = -3.6 \times 10^8 \, \text{N} \][/tex]

So, the electric force acting between the two charges is [tex]\(-3.6 \times 10^8 \, \text{N}\)[/tex].

Therefore, the correct answer is:

B. [tex]\(-3.6 \times 10^8 \, \text{N}\)[/tex]

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