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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)`.

A

`(lamda v )/( 4pi ^(2) epsi _(0) a ) hatj`

B

`(- lamda^(2) v )/(4 pi ^(2) epsi _(0) a ^(2)) hatk`

C

`(-lamda ^(2) v )/(4pi ^(2) epsi _(0) a )`

D

`(lamda v)/(4pi epsi _(0) a ^(2)) hati`

Text Solution

Verified by Experts

The correct Answer is:
B
We know that `vec B = ( mu _(0) I )/( 2pi a ) hati =( mu _(0))/( 2pi ) (lamda v )/( a ) hati`
` vecE = ( lamda hatj )/( 2pi epsi _(0) a ) , vecS = (1)/( mu_(0)) [ vecExx vecB]`
`vecS = (1)/( mu _(0)) [ (lamda)/( 2pi epsi _(0) a ) hatj xx ( mu _(0))/( 2pi a ) lamda v hati ]`
`= (lamda ^(2) v )/( 4pi ^(2) epsi _(0) a ^(2))( hatj xx hati ) = ( - lamda ^(2) v )/( 4pi ^(2) epsi_(0) a ^(2)) hatk`
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