To determine the electric flux passing through a Gaussian surface surrounding a [tex]\( +0.075 \, \text{C} \)[/tex] point charge, we need to use Gauss's law. The law states that the electric flux [tex]\(\Phi_E\)[/tex] through a closed surface is equal to the charge enclosed [tex]\(q\)[/tex] divided by the electric constant (also known as the permittivity of free space) [tex]\(\varepsilon_0\)[/tex].
The formula for electric flux, [tex]\(\Phi_E\)[/tex], is given by:
[tex]\[
\Phi_E = \frac{q}{\varepsilon_0}
\][/tex]
Here:
- [tex]\( q = +0.075 \, \text{C} \)[/tex] (the charge enclosed by the Gaussian surface)
- [tex]\( \varepsilon_0 = 8.854187817 \times 10^{-12} \, \text{C}^2 / (\text{N} \cdot \text{m}^2) \)[/tex] (the permittivity of free space)
Substitute the given values into the formula:
[tex]\[
\Phi_E = \frac{0.075 \, \text{C}}{8.854187817 \times 10^{-12} \, \text{C}^2 / (\text{N} \cdot \text{m}^2)}
\][/tex]
Calculate the value:
[tex]\[
\Phi_E \approx 8470568001.2796135 \, \text{N} \cdot \text{m}^2 / \text{C}
\][/tex]
Now, match this result with the given options:
- a) [tex]\(8.5 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}\)[/tex] is very close to our calculated result.
Therefore, the correct answer is:
a) [tex]\(8.5 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}\)[/tex]
