Answered

Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Discover in-depth and trustworthy answers from our extensive network of knowledgeable professionals.

One particle has a charge of [tex]-1.87 \times 10^{-9} \, C[/tex], while another particle has a charge of [tex]-1.10 \times 10^{-9} \, C[/tex]. If the two particles are separated by 0.05 m, what is the electromagnetic force between them?

The equation for Coulomb's law is [tex]F_e = \frac{k q_1 q_2}{r^2}[/tex], and the constant, [tex]k[/tex], equals [tex]9.00 \times 10^9 \, N \cdot m^2 / C^2[/tex].

A. [tex]-7.41 \times 10^{-6} \, N[/tex]
B. [tex]-3.70 \times 10^{-7} \, N[/tex]
C. [tex]7.41 \times 10^{-6} \, N[/tex]
D. [tex]3.70 \times 10^{-7} \, N[/tex]

Sagot :

GinnyAnsweridn
To find the electromagnetic force between the two particles, we'll use Coulomb's law, which is given by the formula:

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

where:
- [tex]\(k\)[/tex] is Coulomb's constant, [tex]\(9.00 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2\)[/tex],
- [tex]\(q_1\)[/tex] and [tex]\(q_2\)[/tex] are the charges of the particles,
- [tex]\(r\)[/tex] is the separation distance between the charges.

Given data:
- [tex]\( q_1 = -1.87 \times 10^{-9} \, \text{C} \)[/tex]
- [tex]\( q_2 = -1.10 \times 10^{-9} \, \text{C} \)[/tex]
- [tex]\( r = 0.05 \, \text{m} \)[/tex]

Now substitute these values into the formula:

[tex]\[ F_e = \frac{(9.00 \times 10^9) \times (-1.87 \times 10^{-9}) \times (-1.10 \times 10^{-9})}{(0.05)^2} \][/tex]

First, calculate the numerator:

[tex]\[ (9.00 \times 10^9) \times (-1.87 \times 10^{-9}) \times (-1.10 \times 10^{-9}) \][/tex]

The product of the charges ([tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex]) will be positive because multiplying two negative numbers yields a positive result. Simplifying this, we get:

[tex]\[ (9.00 \times 10^9) \times (1.87 \times 10^{-9}) \times (1.10 \times 10^{-9}) = 9.00 \times 1.87 \times 1.10 \times 10^9 \times 10^{-9} \times 10^{-9} \][/tex]

[tex]\[ = 9.00 \times 1.87 \times 1.10 \times 10^{-9} \][/tex]

Next, calculate the denominator:

[tex]\[ (0.05)^2 = 0.0025 \][/tex]

Now substitute these into the expression for [tex]\( F_e \)[/tex]:

[tex]\[ F_e = \frac{9.00 \times 1.87 \times 1.10 \times 10^{-9}}{0.0025} \][/tex]

Calculate the values:

[tex]\[ 9.00 \times 1.87 = 16.83 \][/tex]

[tex]\[ 16.83 \times 1.10 = 18.513 \][/tex]

[tex]\[ F_e = \frac{18.513 \times 10^{-9}}{0.0025} \][/tex]

[tex]\[ F_e = 18.513 \times 10^{-9} \times \frac{1}{0.0025} \][/tex]

[tex]\[ F_e = 18.513 \times 10^{-9} \times 400 \][/tex]

[tex]\[ F_e = 7.4052 \times 10^{-6} \, \text{N} \][/tex]

Therefore, the electromagnetic force between the two particles is:

[tex]\[ \boxed{7.41 \times 10^{-6} \, \text{N}} \][/tex]

So the correct answer is:

C) [tex]\(7.41 \times 10^{-6} \, \text{N}\)[/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.