# Gauss's law in deducing electric field on surface of a sphere conductor

We know that the electric field inside and outside of a spherical conductor is given by $$0$$ and $$\frac{kq}{r^2}$$ respectively. The 2nd formula is derived using Gauss's law by creating a spherical gaussian surface at the distance we are interested in. But Gauss's law states that the flux is $$\frac{q_{\mathrm{inside}}}{\epsilon_0}$$. But if we consider the sphere itself as the gaussian surface forthe distance $$r=R$$,we are assuming that a charge $$q$$ is inside the surface whereas the charge $$q$$ is on the surface. So no $$q_{\mathrm{inside}}$$ exists in this case. How are we then still being able to apply the Gauss law?

Below I have attached a picture of an article claiming that the result is actually $$\frac{kq}{2R^2}$$. Now I am really confused since untill this day I knew it to be $$\frac{kq}{R^2}$$ but didn't know the proof. Kindly clear this confusion.

• Complete article Nov 16, 2022 at 8:14
• I have that article,asking for article wasn't my intention Nov 16, 2022 at 10:07
• Nov 16, 2022 at 10:17
• Related (2) : Trajectory of electric field lines. Nov 16, 2022 at 10:18
• I didn’t post the article for you. I posted it for other readers who might want to read more of the calculation than you posted. Nov 17, 2022 at 7:25