Show that in an electromagnetic wave average energy density of the electric field `bar(E)` equals the average energy density of the magnetic field `bar(B)`

Explanation

Average energy density of E
`U_(E)=(1)/(4)epsi_(0)E_(0)^(2)`
Average energy density of B
`U_(B)=(1B_(0)^(2))/(mu_(0))`
`:. c=(E_(0))/(B_(0))` So,
`U_(E)=(1)/(4)epsi_(0)(cB_(0))^(2)=(1)/(4)epsi_(0)c^(2)B_(0)^(2)=(1)/(4)epsi_(0)(1)/((mu_(0)epsi_(0)))xxB_(0)^(2)`