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Question
An infinitely long thin wire carrying a uniform linear static charge density λ is placed along the z-axis (figure). The wire is set into motion along its length with a uniform velocity `v = vhatk_z`. Calculate the poynting vector `S = 1/mu_0 (E xx B)`.
Solution
The electric field due to infiniety long thin wire `vecE = (λhate_s)/(2piε_0a) hatj`
Magnetic field due to the wirem `vecB = (mu_0i)/(2pia) hati`
Equivalent current flowing through the wire, `i = λv`
Hence `vecB = (mu_0λv)/(2pia) hati`
∴ `vecS = 1/mu_0 [vecE xx vecB] = 1/mu_0 [λ/(2piε_0a) hatj xx (mu_0λv)/(2pia) hati]`
= `(-λ^2v)/(4pi^2ε_0a^2) hatk`
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