Question

retric field of radiation inside a hollow rectangular waveguide whose geometry is sketched below, has the following form: E., - , xeyal sind 5). ---, E, -E --O; where y-(0)* -o uso so and the other symbols have the where y = > 0 and the other symbols have their usual meaning N ds a) Derive expressions for the three Cartesian components of the magnetic field of radiation inside the guide. b) Calculate the average power flowing across any plane transverse to the x-direction. Provide a simple physical explanation for your answer.

Answer 1

utora . Ans:- Ex= Ez=0, Ey & Who Hob sin ( 6 Ads > a - G E = - + , , *** BEZ 052)+(*293) . z / jut-8x7 (- 2EL) + (0) th (Den) = 1 E h DEL -- [5 w Ho Hob (T ) cos(CZ Jesut_42741 [Ho Hob sin(+3) (8) etwt - sx] --( w lotto cos foi Jesut-**) - ? why hab sin (1) Now, - 2B - ZE -> @ I sw Holto cus (7) ébut -4x] +ê [ * wwe to b4 sin(13) exwte-4x] integrating w.rt. t: B = î j w Molto) cus(17) esut -40 + 2 ls Who Hober) sin(77) elow) 2 ? Motto cos (TZ) e sub-8x + 2 Molto by sin (Z). so, Box= do Ho cos (+7) e jwt-4x By Bz = Molto be sin (TZ) swt - 8x eiuf (sw) engal - Who Hobs +12 ITZ leworth T jut-4x By=o,

T- (6) = ý juro Hob sin (IZ Je swt - 4r. B = 2 Motto cos (Z) e iwt-4x + 4o Hoby sin (47) e sust-wa porynting veeter: - Ex B + (-2) t who Hob & Mo Ho sin (TZ) cos (17 e 217 ) + (2) Judo Hob x Motto by sin? (172) e 21 wt-4x)] - - *w po tayong in(tz Secas (az) e 265w) +ê jw (hob mo et sin (mg) e 213ud-40) J T2