You may wish to review Sections 16.5 and 17.3 on the

Chapter 34, Problem 70

(choose chapter or problem)

You may wish to review Sections 16.5 and 17.3 on the transport of energy by string waves and sound. Figure P34.15 is a graphical representation of an electromagnetic wave moving in the x direction. We wish to find an expression for the intensity of this wave by means of a different process from that by which Equation 34.24 was generated. (a) Sketch a graph of the electric field in this wave at the instant t 5 0, letting your flat paper represent the xy plane. (b) Compute the energy density uE in the electric field as a function of x at the instant t 5 0. (c) Compute the energy density in the magnetic field uB as a function of x at that instant. (d) Find the total energy density u as a function of x, expressed in terms of only the electric field amplitude. (e) The energy in a shoebox of length l and frontal area A is El 5 el 0 uA dx. (The symbol El for energy in a wavelength imitates the notation of Section 16.5.) Perform the integration to compute the amount of this energy in terms of A, l, Emax, and universal constants. (f) We may think of the energy transport by the whole wave as a series of these shoeboxes going past as if carried on a conveyor belt. Each shoebox passes by a point in a time interval defined as the period T 5 1/f of the wave. Find the power the wave carries through area A. (g) The intensity of the wave is the power per unit area through which the wave passes. Compute this intensity in terms of E max and universal constants. (h) Explain how your result compares with that given in Equation 34.24.