A plane EM wave travelling in vacuum along z direction is given by and

(i) Evaluate over the rectangular loop 1234 shown in Fig 8.2.



(ii) Evaluate over the surface bounded by loop 1234.


(iii) Use equation to prove .


(iv) By using similar process and the equation , prove that



i) the electromagnetic wave is propagating in z direction; the direction of electric field is along x axis and for magnetic field it is along y axis



The integration along the rectangular loop 1234 is given by,





This is the value of integral .


ii) For calculating , consider a small strip of area ds = h dz






iii)


Given that:



Substituting the value obtained in part i and ii we get,








iv) Consider the loop 1234 in the plane y-z,






Now consider the strip of area h.ds in the rectangle 1234.







Given:


Where, I = conduction current


For vacuum I = 0



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