An infinitely long thin wire carrying a uniform linear

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

$\vec{S}=\frac{\lambda^{2} v}{4 \pi^{2} \epsilon_{0} a^{2}} \hat{k}$