Question

A parallel plate capacitor having a plate separation on $2mm$ is charged by connecting it to a $300V$ supply. The energy density is:

• A. $0.01J/m^3$
• B. $0.1J/m^3$
• C. $1.0J/m^3$
• D. $10J/m^3$

Answer 1

Answer: (B)

Energy density in the energy per unit volume.
The energy per unit volume or the energy density is given, by,
$U=\frac{1}{2}{\epsilon }_0{E}^2\dots (1)$
Where ${\epsilon }_0$ is permittivity of free space and $E$ is electric field.
Also $E=\frac{V}{d}\dots (2)$
$=\frac{\text{ Potential difference }}{\text{ Distance between the plates }}$
From Eqs. (1) and (2), we have
$U=\frac{1}{2}{\epsilon }_0{\left(\frac{V}{d}\right)}^2$
Given, $V=300$ Volt,
$d=2mm$
$=2\times 10^{-3}<br/>,m$,
${\epsilon }_0=8.85\times 10^{-12}{C}^2/N{m}^2$
$\therefore U=\frac{1}{2}\times 8.85\times 10^{-12}\times {\left(\frac{300}{2\times 10^{-3}}\right)}^2$
$U=0.1J/m^3$
Note: We can also say that if electric field $\vec{E}$ exists in some space, then the space is a store of energy whose amount per unit volume is equal to energy density.