Question

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

Answer 1

\[\LARGE \dfrac{1}{2} \epsilon_0 E^2\]

Answer 2

@Vincent-Lyon.Fr

Answer 3

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.