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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(B).vec(d)s` over the surface bounded by loop 1234.

Text Solution

Verified by Experts

Let square 1234 is made up of very large no. of small strip ds, let area of one strip = ds = h dz
`therefore int vec(B ).vec(d)s=int B ds cos 0^(@)`
`= int B ds " " [because cos 0^(@)=1]`
`= int_(z_(1))^(z_(2))B_(0)sin (kz- omega t)h dz " " [because ds = h dz]`
`=-(B_(0)h)/(k)`
`[cos(kz_(2)-omega t)-cos (kz_(1)-wt)] " "` ....(2)
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