11.58. ATM uniform plane wave traveling in the +x direction in free space is…

11.58. ATM uniform plane wave traveling in the +x direction in free space is incident normally on a lossless dielectric circular cylinder of radius a, as shown in Figure sigure P11-58. Assume that the incident, scat- tered, and transmitted into the cylinder) electric fields can be written as (a) Derive expressions for the incident, scattered, and transmitted magnetic field components. (6) (b) Show that the wave amplitude coeffi- cients are equal to Cn = 0 +00 E’ = az Eo ;-“J,(Bop)eing +0 E’ = â: Eo i 4,4,2(Bop)ejnos J(Boa)Jn (Ba) -Ver/upJn (Boa)JK(Bia) Ver/urJn (Ba)H,2)(Boa) -In(Ba)H,2) (Boa) Jn (Boa)H,P) (Boa) – Ly (Boa)H,2) (Boa) Jn (Ba),- (Boa) – Jer/ur * J, (Ba)h,2′ (Boa) =- +00 bn =j-” E’ = â, Eo [bnJn (Bip) + cnY,(Bip)]ejno n=-00 / Eo, Mo & roll, HA Figure P11-58