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Poynting vectors vec(S) is defined as ve...

Poynting vectors `vec(S)` is defined as `vec(S)=(1)/(mu_(0))vec(E)xx vec(B)`. The average value of `'vec(S)'` over a single period 'T' is given by

A

`E_(0)^(2)//2cmu_(0)`

B

`E_(0)^(2)//cmu_(0)`

C

`2E_(0)2^(2)//c mu_(0)`

D

`E_(0)^(2)//cmu_(0)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Poynting vector is given by, `vecS=(vecExxvecB)/(mu_(0))`
Average value of magnitude of radiant flux density over one cycle is
`S_(av)=(1)/(mu_(0))|vecE_(0)xxvecB_(0)|((1)/(T))int_(0)^(T)cos^(2)(kx-omegat)dt`
`[becauseE=E_(0)cos(kx-omegat),B=B_(0)cos(kx-omegat)]`
`=(E_(0)B_(0))/(mu_(0))((1)/(T))(T//2)=(E_(0)B_(0))/(2mu_(0))[becauseint_(0)^(T)cos^(2)(kx-omegat)dt=T//2]`
`s_(av)(E_(0)(E_(0)//c))/(2mu_(0))=((1)/(2cmu_(0)))E_(0)^(2)" "(becauseB_(0)=(E_(0))/(c))`
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