Question

Problem 5 (20pts). The magnetic field of an electromagnetic wave propagating in free space is given by: H(R,6,t) = (@0.2653 + $0.5305) sinėsin(wt – kR), Ho = 41 x 10-7 (H/m), €, = 8.85 x 10-12 (F/m). Frequency of 150 x 106 Hz Hint: useĚ = 1vx jw Find: a) Ễ (R,Q) and E(R,6,t), Let în component equal zero b) value of k

Answer 1

of where we know from the Maxwell's fourth equation Classical electromagnetic field in free space öx } + to az It It is the magnetic fiels , J is the current dousity and pē is the rate of change of electric flux in free space. In this particular problem, ot J is zero . VXH - م Resina He It As it (R. 8st) is given, we will start from the Left Homo size, from the Curvilineas Coordinates the care of a physical quantity in spherical Coordinates com be written as: Ex H - R Rsmo %r %o %0 Rho Rsnio HQ Where the general form is : EX Ă s. 1 hê } Where hi ha, hz are chicha hin l %ou fous Yous 'Seale factors which takes &, Au, hy Au 4, Au, the form e,= 1, har hz=rsnice in spherical coordinate system and fui, as, ilg} = {2,0,0} tere Ŕ component is zero Ex t = 1 smie R?snio alo n hre ho EN Ro %r %Q. 0 RHO Rsmo Ho where Hot 0.7653 R 0.5305 smo siri (wt = KR) smo sim (wt-KR) Hq

(11) value of x :. In free space k= to low? k2 or ka Go lo > tollo x w W² but we know ² L toleo 2) ez V.to lo Where e is the speed of light 3X100 m/s ko w 21f > - © 310 C ke 20 * 158 x 10 3x108 2T X 15 3 X ID > 30 TT 21 30