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

Question

Philoid · Accepted Answer

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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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