(4) 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)r - (2.51 x 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 x 10-9 J/m". How many Joules from the pulse does the dish absorb? (c) The Sun has a surface temperature of 5770 K, a radius of 6.96 x 105 km, an average distance from Earth of 1.196 x 108 km, and radiates c/m radiation into space isotropically. Earth is a sphere with a radius of 6378 km, and on average reflects 30 percent of the sunlight that shines on it back into space, and absorbs the rest. Both the Sun and Earth are opaque to e/m radiation of all wavelengths, so intensity I = oT, where o is the Stefan-Boltzmann constant (with o = 5.67 x 10-8 W/(m' K1)) and T is Kelvin temperature. Calculate the average temperature (in Kelvins) of Earth. (The next page is blank, so you may write answers there. You may also write answers on this page.)