(a)
The frequency of an electromagnetic waves is given by:
where
is the speed of light
is the wavelength of the wave in the problem
Substituting into the equation, we find
(b)
The angular frequency of a wave is given by
where
f is the frequency
For this wave,
So the angular frequency is
(c)
The angular wave number of a wave is given by
where
is the wavelength of the wave
For this wave, we have
so the angular wave number is
(d)
For an electromagnetic wave,
where
E is the magnitude of the electric field component
c is the speed of light
B is the magnitude of the magnetic field component
For this wave,
E = 310 V/m
So we can re-arrange the equation to find B:
(e) z-axis
In an electromagnetic wave, the electric field and the magnetic field oscillate perpendicular to each other, and they both oscillate perpendicular to the direction of propagation of the wave. Therefore, we have:
- direction of propagation of the wave --> positive x axis
- direction of oscillation of electric field --> y axis
- direction of oscillation of magnetic field --> perpendicular to both, so it must be z-axis
(f) 127.5 W/m^2
The time-averaged rate of energy flow of an electromagnetic wave is given by:
where we have
E = 310 V/m is the amplitude of the electric field
is the vacuum permeability
c is the speed of light
Substituting into the formula,
(g)
For a surface that totally absorbs the wave, the rate at which momentum is transferred to the surface given by
where the <S> is the magnitude of the Poynting vector, given by
and where the surface is
A = 1.8 m^2
Substituting, we find
(h)
For a surface that totally absorbs the wave, the radiation pressure is given by
where we have
Substituting, we find
