How do we get average energy density as
$$\LARGE \dfrac{1}{2} \epsilon_0 E^2$$

Question

How do we get average energy density as
 $$\LARGE \dfrac{1}{2} \epsilon_0 E^2$$

aravindg · Answer

$$\LARGE \dfrac{1}{2} \epsilon_0 E^2$$

aravindg · Answer

@Vincent-Lyon.Fr

vincent-lyon.fr · Answer

The easiest way is to rewrite electric energy in a capacitor EE = (1/2)CU²
using electric field E = U/d and capacitance C = $\epsilon_0$A/d

You will end up with EE = $\dfrac {\epsilon_o\,E^2}{2}\times Ad$ giving density   $u_e=\dfrac {\epsilon_o\,E^2}{2}$


Full derivation can be obtained from conservation of energy carried by an electromagnetic wave from Maxwell's equations, but requires more complicated differential mathematics.