Answer to Question #217473 in Electricity and Magnetism for Pilot

Question

Apply gauss's theorem to calcutta the electric field in the case of a changed infimite plan

Answer 1

Gaussian surface total output flux

$$\phi=\smallint_{s_1}E.ds+\smallint_{s_2}E.ds+\smallint_{s_3}E.ds$$

s₃ surface Eand ds is perpendicular

$\theta=90°$

$\smallint_{s_3}E.ds=\smallint_{s_3}E.dscos\theta\\\smallint_{s_3}E.dscos90=0$

$s_1,s_3$ Surface are E and ds are same direction

$\theta=0°$

$$\phi=\smallint_{s_1}E.dscos\theta+0+\smallint_{s_3}E.dscos\theta\\\phi=2ES\rightarrow(1)$$

Gauss law

$\phi=\frac{q}{\epsilon_0}\rightarrow(2)$

Surface charge density

$\sigma=\frac{q}{S}\\q=\sigma S \rightarrow(3)$

equation (1),(2),(3) we can written as

$E=\frac{\sigma}{2\epsilon}$