Electric field from a uniformly charged infinite plane sheet

1)Suppose Z is a thin plane charge sheet with surface charge density σ.

2)Now we draw a closed surface like a cylinder as shown in the diagram.



3) Here there is no electric flux along the surface A & D, because

 surface direction  is normal to the electric field.


4)So there will have only two surfaces where electric flux are passing B & C, but both have equal area say X.

5) therefore total surface area where flux is passing are

6)Now the enclosed surface on the thin charge sheet is also X.

7)Therefore total charge enclosed by the surface is

total charge = σ X    ------ (1.27)

8) now we know that electric flux is



9) From Gauss’s law, and putting the value of total charge from (1.27)



Now putting the value 

of from (2.37)


Therefore