# Two large parallel plane sheets have uniform charge densities $+\sigma$ and $-\sigma$. Determine the electric field (i) between the sheets, and (ii) outside the sheets.

Let us consider the two parallel sheets A and B of charges $+\sigma$ and $-\sigma$ and the points P,Q,R.

Now, the electric field due to the plane sheet of charge is given as

$E=\frac{\sigma }{2\varepsilon _{o}}$

Where, $\sigma$ is the surface charge density.

Such that,

$E_{A}=+\frac{\sigma }{2\varepsilon _{o}}$ and $E_{B}=-\frac{\sigma }{2\varepsilon _{o}}$

then,

(i) The electric field between the sheets at point Q is ;

$\vec{E}=\vec{E}_A-\vec{E}_B$

$=\frac{\sigma }{2\varepsilon _{o}}- (-\frac{\sigma }{2\varepsilon _{o}})$

$=\frac{2}{2}(\frac{\sigma }{\varepsilon _{o}})$

$\vec{E}=\frac{\sigma }{\varepsilon _{o}}$

(ii) The electric field outside the sheets at point P or P

$\vec{E}=\vec{E}A+\vec{E}B$

$\vec{E}=\frac{\sigma }{2\varepsilon _{o}}- \frac{\sigma }{2\varepsilon _{o}}$

$\vec{E}=0$

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