In a plane Electromagnetic wave the electric field oscillates sinusoidally at a frequency of `2.0 X 10^(10)` Hz & amplitude 48 `Vm^(-1)`.
show that the average energy density of the electric field `(vec(E ))`, is equal to average energy density of the magnetic field `(vec(B))`

Explanation

Average energy magnetic field `vec(E )`
`U_(E ) " " (1)/(2) cdot epsilon_(0) E^(2) `
Average energy density of electric field `vec(B)`
`U_(E ) = (1)/(2 mu_(0)) cdot B^(2)`
But E = CB & `C^(2) = (1)/(mu_(0)epsilon_(0))`
`U_(E ) = (1)/(2) cdot epsilon_(0) E^(2) = (1)/(2) cdot epsilon_(0)(CB)^(2)`
`U_(E ) = (1)/(2) cdot epsilon_(0) (1)/(mu_(0)epsilon_(0)) B^(2) = (1)/(mu_(0) epsilon_(0)) B^(2) = U_(B)`
`therefore U_(E ) = U_(B)`