# Two large charged plane sheets of charge densities $\sigma$ and $-2\sigma \; C/m^{2}$ are arranged vertically with a separation of d between them. Deduce expressions for the electric field at points (i) to the left of the first sheet, (ii) to the right of the second sheet, and (iii) between the two sheets.

Deducing electric field in the region left of the sheet that is the region I

$E_{I}=E_{1}+E_{2}$

$E_{I}=\frac{\sigma }{\varepsilon _{o}}-\frac{\sigma }{2\varepsilon _{o}}$

$E_{I}=+\frac{\sigma }{2\varepsilon _{o}}$

It is towards the right

The electric field in region II is

$\\E_1+E_2=\frac{\sigma}{2\epsilon_0}-\frac{2\sigma}{2\epsilon_0}=-\frac{\sigma}{2\epsilon_0}$

Towards left

Now, deducing electric field between the two sheets.

$E_{III}=E_{I}+E_{II}$

$E_{III}=\frac{\sigma }{\varepsilon _{o}}+\frac{\sigma }{2\varepsilon _{o}}$

$E_{III}=\frac{3\sigma }{2\varepsilon _{o}}$   Here, the electric field is towards the right.

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