question_answer 45)

    A plane EM wave travelling in vacuum along z direction is given by  and                                          (i) Evaluate dl over the rectangular loop 1234 shown in Fig. 5(EP).4.  (ii) Evaluate over the surface bounded by loop 1234.  (iii) Use equationto porve (iv) By using similar process and the equation , prove that

Answer:

                  (i) During the propagadon of electromagnetic wave along z-axis, let electric field vector   be along .x-axis and magnetic field vector  be along y-axis, i.e.,  and Refer Fig. 5(EP).5. Line integral of  over the closed rectangular, path 1234 in x-z plane is =                                                            ?(i)  (ii) For evaluating over the surface bounded by loop 1234, let us consider a rectangle 1234 be made of small strips. One small strip of area ds = h dz. is shown in Fig. 5(EP).6.                 Surface bounded by strips 1234                 ?(ii) (iii) Give, Putting the values from (i) and (ii), we get Or                  (iv) For evaluating  , let us consider a loop 1342 in y-z plane as shown in Fig. 5(EP).7.                                            ?(iii) To evaluate, let us consider the rectangle 1342 to be made up of strips, each of area. Fig . 5  (EP) .8.                                                                                                                                                                   ?(iv)                 In the relation,  is the conduction current. The value of  = 0 (in vacuum).                                                            Putting values from (iii) and (iv), we get                 or    or                            Or                           Or