a) Calculate the speed of the radiation. Don’t assume it must be equal to c: use the equation above to calculate this speed. (b) Calculate the amplitude of the magnetic field of this wave. (c) Calculate the Poynting flux of the radiation.
A dish antenna with a diameter of 15.0 m receives a beam of radio radiation at normal incidence. The
radio signal is a continuous wave with an electric field given by:
E = 0.75 sin[(0.838/m)x − (2.51 × 108
/s)t] N/C.
Here, x is in meters and t is in seconds. Assume that all the radiation that falls on the dish is absorbed.
(a) Calculate the speed of the radiation. Don’t assume it must be equal to c: use the equation above to
calculate this speed.
(b) Calculate the amplitude of the magnetic field of this wave.
(c) Calculate the Poynting flux of the radiation.
(d) Suppose the beam that is entering this dish has the same diameter as the dish. Suppose a pulse of
radiation that lasts for 10.0 ns travels along the beam and into the dish. This pulse has an energy density of
1.0 × 10−9 J/m
3
. How many Joules from the pulse does the dish absorb?
(e) The Sun has a surface temperature of 5770 K, a radius of 6.96 × 105 km, an average distance from Earth of
1.496 × 108 km, and radiates e/m radiation into space isotropically. Earth is a sphere with a radius of 6378 km,
and on average absorbs 30 percent of the sunlight that shines on it, with the rest reflected back into space.
Both the Sun and Earth are opaque to e/m radiation of all wavelengths, so intensity I = σT4
, where σ is the
Stefan-Boltzmann constant and T is Kelvin temperature. Calculate the temperature (in Kelvins) of Earth.
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