Poynting Vector Problem Solution

 Problem:

 A radio wave transmits 25 W/m ² of power per unit area. A plane surface of area 2.4 m x 0.7 m is perpendicular to the direction of propagation of the wave. Calculate the radiation pressure  P _R  on the surface if it is assumed to be a perfect absorber.

Solution:

The intensity of an EM wave is :  I = S(av) =

E _max B _max/ 2 m_o

where the area A = 2.4 m x 0.7 m = 1.68 m ²  and P _R  denotes the radiation pressure, or   P _R = S/c (for complete absorption)

Now, S = (Power/ area )=  ( 25 W/m ² ) / (1.68 m ²)

 Then:

S =   14.88 W

And the radiation pressure: 

P _R = S _av / c = 14.88 W/ (3 x 10 ⁸ m/s)

= 3.3 x 10  ^{- 9}  N/m²