Answer to Question #185219 in Field Theory for Esmail

Question

Use Gauss’ Law to calculate the electric field due to an infinite non-conducting sheet of charge, with surface charge density 

Answer 1

Answer

Consider a non conducting sheet with charge density $\sigma$

By gauss law flux of it

$\phi=\frac{\sigma s}{\epsilon_0}$

And by definition

$\phi=\int Edscos0°+\int Eds cos0°$

So

$\frac{\sigma s}{\epsilon_0}=2Es\\E=\frac{\sigma }{2\epsilon_0}$