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An infinitely long thin wire carrying a uniform linear

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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