Question

Derive an expression for electric field intensity at a point close and outside the surface of charged conductor of any shape.

Answer 1

Let's consider a uniform charged conductor of any shape. Let $\sigma$ is the surface charge density of its surface. consider a point A very close to the surface of conductor. Take and element dS near the point A, construct an imaginary gaussian surface of Corsa section area dS partially inside and partially outside the conductor as shown in figure.

electric field intensity inside of conductor is zero because there is not electric flux inside the conductor.

electric field intensity outside of conductor is given by, $\textbf{electric flux} = \frac{dq}{\epsilon_0}$
here, $dq=\sigma.dS$
and electric flux = E.dS

so, $E.dS=\frac{\sigma.dS}{\epsilon_0}$

$E=\frac{\sigma}{\epsilon_0}$