Question:
An infinitely long thin wire carrying a uniform linear static charge density λ is placed along the z-axis. The wire is set into motion along its length with a uniform velocity
$v=v \hat{k}_{z} \quad .$ Calculate the pointing vectors $S=1 / \mu_{0}$ (ExB).
Solution:
The electric field in an infinitely long thin wire is
$\vec{E}=\frac{\lambda \hat{e}_{s}}{2 \pi \epsilon_{0} a} \hat{j}$
Magnetic field due to the wire is
$\vec{B}=\frac{\mu_{0} i}{2 \pi a} \hat{i}$
The equivalent current flowing through the wire is
$\vec{S}=\frac{\lambda^{2} v}{4 \pi^{2} \epsilon_{0} a^{2}} \hat{k}$
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