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An infinitely long thin wire carrying a...

An infinitely long thin wire carrying a uniform linear static charge density `lambda` is placed along the z-axis Fig. The wire is set into motion along its length with a uniform velocity `vecv=vhatk`. Calculate the poynting vector `vecS=1/(mu_0)(vecExxvecB)`.

Text Solution

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`vecE=lambda/(2pi in_0a)hatj , vecB=(mu_0)/(4pi) (2I)/ahati =(mu_0)/(2pi) (lambdav)/ahati [ :' I=lambdav]`
`:. S= 1/(mu_0) [vecExxvecB] =1/(mu_0)[(lambdahatj)/(2pi in_a)xx(mu_0)/(2pia)lambdavhati]`
`=(lambda^2v)/(4pi^2in_0a^2)(hatjxxhati)`
`=-(lambda^2v)/(4pi^2in_0a^2)hatk`
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