Question
A large conducting plane has a surface charge density $1.0\times10^{-4}\text{Cm}^{-2}.$ Find the electrostatic energy stored in a cubical volume of edge 1.0cm in front of the plane.
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Answer
$\sigma=1\times10^{-4}\text{c/m}^2$
$\text{a}=1\text{cm}=1\times10^{-2}\text{m}$
$\text{a}^3=10^{-6}\text{m}$
The energy stored in the plane $=\frac{1}{2}\frac{\sigma^2}{\in_0}=\frac{1}{2}\frac{(1\times10^{-4})^2}{8.85\times10^{-12}}$
$=\frac{10^4}{17.7}=564.97$
The necessary electro static energy stored in a cubical volume of edge 1cm infront of the plane $=\frac{1}{2}\frac{\sigma^2}{\in_0}\text{a}^3=265\times10^{-6}=5.65\times10^{-4}\text{J}$
$\text{a}=1\text{cm}=1\times10^{-2}\text{m}$
$\text{a}^3=10^{-6}\text{m}$
The energy stored in the plane $=\frac{1}{2}\frac{\sigma^2}{\in_0}=\frac{1}{2}\frac{(1\times10^{-4})^2}{8.85\times10^{-12}}$
$=\frac{10^4}{17.7}=564.97$
The necessary electro static energy stored in a cubical volume of edge 1cm infront of the plane $=\frac{1}{2}\frac{\sigma^2}{\in_0}\text{a}^3=265\times10^{-6}=5.65\times10^{-4}\text{J}$
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