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

E = Eo sin(kz –ωt )i and B=Bosin (kz ωt)j .

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

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

(iii) Use equation E.dl=-dϕB/dt to prove Eo/Bo=c.

(iv) By using similar process and the equation

B.dl= μoI+ɛdϕE/dt, prove that c=1/μoɛo 

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(ii) For evaluating B.ds let us consider the rectangle 1234 to be made of strips of area ds = h dz each.

Using the relations obtained in Equations (1) and (2) and simplifying, we get

(iv) For evaluating NB.dl , let us consider the loop 1234 in yz plane as shown in Fig.

Now to evaluate ϕE = E.ds , let us consider the rectangle 1234 to be made of strips of area hdz each.

Using relations obtained in Equations (3) and (4) and simplifying, we get

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