Flux and Gauss's law in code

You will write three small functions about flux. They use $\Phi = EA\cos\theta$ and Gauss's law.

The idea. The flux of a uniform field through a flat surface is $EA\cos\theta$, with $\theta$ the angle with the normal. The net flux through a closed surface is $q_{\text{in}}/\varepsilon_0$, and only the charges inside count. Take $\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2/(\text{N m}^2)$.

Your tasks.

1. In flat_flux, return the flux in N m²/C. The field E is in N/C, the area A in m², and angle is in degrees.
2. In net_flux, charges is a list of pairs (charge in nC, inside), where inside is True or False. Return the net flux in N m²/C. Count only the charges that are inside.
3. In charge_from_flux, return the net charge in nC that gives the net flux flux.