Question

4) Consider two material media separated by the boundary surface at z-0. The region 1, z> 0 has a uniform electric field given by E! a.20-?-50. obtain a). ?2in medium 2 b) Jand J2 and ch the angle and J2 make with the xz plane 15ms 2 S

Answer 1

Given, E_1 = 20 a_x - 50 a_z epsilon_1 = 2 epsilon_0 epsilon_2 = 3 epsilon_0 Since, a_z is normal to the boundary plane, E_1n = E_1 middot a_n = E_1 middot a_z = -50 Therefore E_1 n = -50 a_z E_1 = E_1t + E_tn => E_1t = E_1 - E_1n = (20 a_x - 50 a_z) - (-50 a_z) = 20 a_x From boundary conditions, E_1 t = E_2t D_1n = D_2n => E_1t = E_2 t = 20 a_x => D_1n = D_2 n epsilon_1 E_1n = epsilon_2 E_2n => E_2n = epsilon_1/epsilon_2 middot E_3n = 2/3 E_1n = -100/3 a_z Therefore E_2 = E_2 t + E_2n = 20 a_x - 100/3 a_z Let alpha_1, alpha_2 be the angles making with interface and theta_1, theta_2 with normal \r\n E_1 n = -50 E_1 t = 20 Therefore tan theta_1 = E_1t/E_2n = 20/- 50