(Solution) - A very large flat sheet carries -(2025 Original AI-Free Solution)

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A very large flat sheet carries a uniformly distributed electric current with current per unit width Js. Example 30.6 demonstrated that the current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B=½?0Js. If the current oscillates in time according to Js = J max (cos wt)j = J max [cos (- wt)]j, the sheet radiates an electromagnetic wave as shown in Figure P34.37. The magnetic field of the wave is described by the wave function B = ½ ?0J max [cos (kx - wt)] k.
(a) Find the wave function for the electric field in the wave.
(b) Find the Poynting vector as a function of x and t.
(c) Find the intensity of the wave.
(d) What If? If the sheet is to emit radiation in each direction (normal to the plane of the sheet) with intensity 570 W/m2, what maximum value of sinusoidal current density is required?