(Solved): The charge is uniformly spread along an infinite conducting wire of radius, \( R=r_{\text {wire }} ...

The charge is uniformly spread along an infinite conducting wire of radius, \( R=r_{\text {wire }} \) mm giving the wire a uniform linear charge density of \( \lambda=\frac{Q}{L} \frac{C}{m} \) as shown above. Use Gauss's law to find an expression for the magnitude of the electric field a distance \( r_{0}=1 \mathrm{~m} \) from the central axis of the wire. \[ \begin{array}{c} |\vec{E}|=0 \frac{N}{C} \\ |\vec{E}|=\frac{k Q}{r_{0}^{2}} \\ |\vec{E}|=\frac{\lambda}{2 \pi \varepsilon_{0} r} \end{array} \] \[ |\vec{E}|=\frac{\lambda}{2 \pi \varepsilon_{0}} \ln \left(\frac{r_{0}}{r}\right) \] Since the wire is a conductor, all of the electric charge is distributed over the outer surface and the electric field interior to \( \mathrm{R} \) is zero.