The electric field in an infinitely long thin wire is given by the expression,
$\vec{E}=\frac{\lambda \hat{e}_{s}}{2 \pi \epsilon_{0} a} \hat{j}$
Magnetic field due to the wire is given by the expression,
$\vec{B}=\frac{\mu_{0} i}{2 \pi a} \hat{i}$
The equivalent current flowing through the wire is given by the expression,
$\vec{s}=\frac{\lambda^{2} v}{4 \pi^{2} \epsilon_{0} a^{2}} \hat{k}$