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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^(2)v)/(4pi^(2)epsilon_(0)a^(2))hat(k)`

B

`(lamda^(2)v)/(4pi^(2)epsilon_(0)a^(2))hat(i)`

C

`(lamda^(2)v)/(4pi^(2)epsilon_(0)a^(2))hat(k)`

D

`(-lamda^(2)v)/(4pi^(2)epsilon_(0)a^(2))hat(i)`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that
`vec(B) = (mu_(0)I)/(2pia) hati = (mu_(0))/(2pi) (lambda v)/(a) hati, vec(E) = (lambda hatj)/(2pi epsilon_(0)a)`
`vec(S) = (1)/(mu_(0)) [vec(E) xx vec(B)]`
`vec(S) = (1)/(mu_(0)) [(lambda)/(2piepsilon_(0)a)hatj xx (mu_(0))/(2pia) lambda v hati]`
`= (lambda^(2)v)/(4pi^(2)epsilon_(0)a^(2)) (hatj xx hati) = (-lambda^(2)v)/(4pi^(2)epsilon_(0)a^(2)) hatk`.
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