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A plane EM wave travelling in vacuum alo...

A plane EM wave travelling in vacuum along z - direction is given by `vec(E )=E_(0)sin (kz - omega t)hat(i)` and `vec(B)=B_(0)sin(kz - omega t)hat(j)`.

Evaluate `int vec(E ). Vec(d)l` over the rectangular loop 134 shown in figure.

Text Solution

Verified by Experts

Consider figure given below,

Electromagnetic waves are propagating in z - direction. Let electric field vector `vec(E )` and `vec(B)` is in x - direction and magnetic field vector is in y - direction.
`therefore vec(E ) =E_(0)hat(i)` and `vec(B)=B_(0)hat(j)`
As shown in figure line integration over square path 1234,
`oint vec(E ). vec(d)l = int_(1)^(2)vec(E ).vec(d)l+ int_(2)^(3)vec(E ).vec(d)l+int_(3)^(4)vec(E ).vec(d)l`
`= int_(1)^(2) Ed l cos 90^(@)+int_(2)^(3)Edl cos 0^(@)+int_(3)^(4)Edl cos 90^(@)+int_(4)^(1)Edlcos 180^(@)`
`therefore oint vec(E ).vec(d)l=E_(0)h " " [sin (kz_(2)-omega t)-sin(kz_(1)-omega t)] " "` ....(1)
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