What is energy density? Write its formula.
(N/A) Energy density is defined as the energy stored per unit volume in an electric field.
For a parallel plate capacitor,the energy stored $U$ is given by $U = \frac{1}{2} CV^2$.
Since $C = \frac{\epsilon_0 A}{d}$ and $V = Ed$,we have $U = \frac{1}{2} (\frac{\epsilon_0 A}{d}) (Ed)^2 = \frac{1}{2} \epsilon_0 A d E^2$.
The volume of the space between the plates is $V_{vol} = Ad$.
Therefore,the energy density $u$ is $u = \frac{U}{V_{vol}} = \frac{\frac{1}{2} \epsilon_0 A d E^2}{Ad} = \frac{1}{2} \epsilon_0 E^2$.
For a parallel plate capacitor,the energy stored $U$ is given by $U = \frac{1}{2} CV^2$.
Since $C = \frac{\epsilon_0 A}{d}$ and $V = Ed$,we have $U = \frac{1}{2} (\frac{\epsilon_0 A}{d}) (Ed)^2 = \frac{1}{2} \epsilon_0 A d E^2$.
The volume of the space between the plates is $V_{vol} = Ad$.
Therefore,the energy density $u$ is $u = \frac{U}{V_{vol}} = \frac{\frac{1}{2} \epsilon_0 A d E^2}{Ad} = \frac{1}{2} \epsilon_0 E^2$.
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