During the class we studied the complex notation. We noted that we need to be careful...

Transcribed Image Text:

During the class we studied the complex notation. We noted that we need to be careful when we compute something which is not linear in E and B. Yet, there is a clever device for finding the time average of a product. Suppose f(F, t) = A cos(k-F-wt+da) and g(F, t) = B cos(k-r-wt + 8b). a) Show that (fg) = (1/2) Re(fg*), where the star denotes complex conjugation and represents a complex function of A. Hint: Note that this only works if the two waves have the same k and w, but they need not have the same amplitude or phase. b) Write the electric and magnetic fields in part b) in problem 1 or part b) in problem 2 in terms of complex functions. c) Compute the energy density and Poynting vector 1 E* 1 (u) = Re ( + -B B), 140 (S) 240 Re (B B), for the wave given in part b) in problem 1 or part b) in problem 2. During the class we studied the complex notation. We noted that we need to be careful when we compute something which is not linear in E and B. Yet, there is a clever device for finding the time average of a product. Suppose f(F, t) = A cos(k-F-wt+da) and g(F, t) = B cos(k-r-wt + 8b). a) Show that (fg) = (1/2) Re(fg*), where the star denotes complex conjugation and represents a complex function of A. Hint: Note that this only works if the two waves have the same k and w, but they need not have the same amplitude or phase. b) Write the electric and magnetic fields in part b) in problem 1 or part b) in problem 2 in terms of complex functions. c) Compute the energy density and Poynting vector 1 E* 1 (u) = Re ( + -B B), 140 (S) 240 Re (B B), for the wave given in part b) in problem 1 or part b) in problem 2.

Answer rating: 100% (QA)

The detailed ... View the full answer