Question

Determine the electric flux through a Gaussian surface that contains 87 protons and 73 electrons.

Answer 1

According to the Gauss's law, the electric flux $\Phi$ through a surface is equal to:

$$\Phi = \dfrac{Q}{\varepsilon_0}$$

where $Q$ is the total charge inside this surface, and $\varepsilon_0 = 8.85\times 10^{-12} F/m$ is the vacuum permittivity. Let $e = 1.6\times 10^{-19} C$ be the elementary charge. Then the total charge inside the surface is:

$$Q = 87e - 73e = 14e = 22.4\times 10^{-19}C$$

And the flux is:

$$\Phi = \dfrac{22.4\times 10^{-19}C}{8.85\times 10^{-12} F/m} \approx 2.5\times 10^{-7}V\cdot m$$

Answer. $2.5\times 10^{-7}V\cdot m$.