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)`.

Answer 1

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`