Q.Obtain the expression for the electric field due to a charged infinite plane sheet.

The electric field at a point outside two oppositely charged parallel sheets of equal charge density is zero.

A single infinite plane sheet of charge density $\sigma$ produces a uniform field of magnitude $\dfrac{\sigma}{2\varepsilon_0}$ on each side, directed away from the sheet if $\sigma$ is positive and towards it if $\sigma$ is negative.

For two parallel sheets facing each other with densities $+\sigma$ and $-\sigma$ (a parallel-plate arrangement):

• Between the plates, the field from the $+\sigma$ sheet (pointing away from it, into the gap) and the field from the $-\sigma$ sheet (pointing towards it, also into the gap) point in the same direction, so they add: $E_{between} = \dfrac{\sigma}{2\varepsilon_0}+\dfrac{\sigma}{2\varepsilon_0}=\dfrac{\sigma}{\varepsilon_0}$. …