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An infinitely long thin wire carrying a uniform linear static charge density \lambda is placed along the z-axis. The wire is set into motion along its length with a uniform velocity  v=v\hat{k}_{z} Calculate the pointing vectors S=\frac{1}{\mu _{0}}\left ( E \times B \right ).


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The electric field in an infinitely long thin wire is

\overrightarrow{E}=\frac{\lambda \hat{e}_{s}}{2\pi \epsilon _{0}a}\hat{j}

Magnetic field due to the wire is

\overrightarrow{B}=\frac{\mu _{0}\lambda v}{2\pi a}\hat{i}

The equivalent current flowing through the wire is

\overrightarrow{S}=\frac{\lambda ^{2}v}{4\pi^{2}\epsilon _{0} a^{2}}\hat{k}

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