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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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`"Give"" " E=(lambdahate_(s))/(2piepsilon_(0) a)hatj`
`B=(mu_(0)i)/(2pi a) hati =(mu_(0)lambdav)/(2pia)hati`
`:." "S=1/mu_(0) [ExxB] =(1)/(mu_(0)) [(lambda_(hati))/(2piepsilon_(0)a)xx (mu_(0))/(2pi a)lambdasqrt(hatj)]`
`=(lambda^(2)V)/(4pi^(2)epsilon_(0)a^(2))(hatjxxhati) =- (lambda^(2)V)/(4pi^(2)epsilon_(0)a^(2))hatk`
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