- #1

archaic

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The electric field created by a conductor at a point $M$ extremely close to it is ##\vec{E}=\vec{E_1}+\vec{E_2}## where ##\vec{E_1}## is the electric field created by such a tiny bit of the conductor that we can suppose it to be a plane, and since ##M## is extremely close to the conductor such that the distance is really small compared to the size of the plane we further ahead assimilate it to an infinite plane and hence ##\vec{E_1}=\frac{\sigma}{2\epsilon_0}## and this is where I block, when we use Gauss' law on an infinite plane we also account for the electric fields on the other side of the cylinder (here our gaussian surface) i.e the part inside the conductor, but in the case of the conductor the electric field inside of it would be ##\vec{0}## and so ##\vec{E_1}## should be ##\frac{\sigma}{\epsilon_0}## (##E \pi r^2 + 0 + 0= \frac{\sigma \pi r^2}{\epsilon_0}##)

(I have no idea why latex isn't processing this ^)

I cannot see where I've gone wrong.