Show that instantaneous energy density in electromagnetic wave is equally divided among electric and magnetic field.

Explanation

Electric field energy density (electric energy per unit volume)
`U_(E)=(1)/(2)epsi_(0)E^(2)` (instananeous electric energy density)...(i)
Magnetic field energy density (magnetic energy per unit volueme)
`U_(M)=(1)/(2)(B^(2))/(mu_(0))` (instantaneous magnetic energy density).....(ii)
From equations (i) and (ii)
`(U_(E))/(U_(M))=((1)/(2)epsi_(0)E^(2))/((1)/(2)(B^(2))/(mu_(0)))=epsi_(0)mu_(0)xx(E^(2))/(B^(2))=(1)/(c^(2))xxc^(2)=1`
`U_(E)=U_(M)`
In electromagnetic wae instantaneous energy density associated with electric with electric and magnetic fiels is equal.
Total instaneous energy density
`U=U_(E)+U_(M)=(1)/(2)epsi_(0)E^(2)+(1)/(2)(B^(2))/(mu_(0))`
`U=epsi_(0)E^(2) or (B^(2))/(mu_(0))`