Suppose we have a stationary positive charge at a point in space that we call $+Q$. We know by definition that the flow of the electrostatic field is given by, in its simplified form,
$$\Phi_S(\vec E)=\vec E \cdot \vec S=ES\cos \alpha=+k_e\frac{Q}{r^2}S\cos \alpha$$
where $S$ is the Gaussian surface and $\alpha$ is the angle formed between the electric field lines and the surface vector $\vec S=S\hat{\bf n}$. Suppose that $N$ are the lines of force of the electrostatic field coming out of the charge $+Q$. How do I prove that
$$\Phi_S(\vec E)=+k_e\frac{Q}{r^2}S\cos \alpha\color{red}{=KN}\iff \Phi_S(\vec E) \propto N$$ where $K$ is a constant of proportionality?
