(Solved): (25\%) Problem 6: A very long, thin wire has a uniform linear charge density of \( -105 \mu \mathr ...

(25\%) Problem 6: A very long, thin wire has a uniform linear charge density of \( -105 \mu \mathrm{C} / \mathrm{m} \). A The electric field in the region near the wire may be expressed as \[ \vec{E}=E_{r} \hat{r} \] where the unit vector is perpendicular to and directed away from the wire. What is the value of \( E_{r} \), in ner wire? \[ E_{r}= \] Hints: \( \underline{1} \) for a \( . \) deduction. Hints remaining: \( \underline{0} \quad \) Feedback: \( 0 \% \) deduction per feedback. -There is a standard formula for the electric field around a cylindrically symmetric charge distribution. It may be obtained using a Gaussian surface which is a cylindrical shell with the same symmetry axis as the charge distribution and noting that the electric field may be expresses as \( \vec{E}=E_{r} \hat{r} \) where the unit vector is perpendicular to and directed away from the symmetry axis.