Question

If the distance between the plates of a capacitor is $d$ and potential difference is $V$ then what is the energy density between the plates?

Answer 1

Energy of a capacitor

$E=\frac{1}{2}C{V}^2...........\left(1\right)$

$C=\frac{A{\epsilon }_0}{d}$

$\because E=\frac{V}{d}$

$V=Ed$

Put all in (1)

$E=\frac{1}{2}\frac{A{\epsilon }_0}{d}{\left(Ed\right)}^2$

$=\frac{1}{2}A{\epsilon }_0{E}^{2}d$

$\because Volume=Ad$

$so,$

$E=\frac{1}{2}{\epsilon }_0{E}^{2}v$

$\frac{E}{v}=\frac{1}{2}{\epsilon }_0{E}^2$