By using a cylindrical surface of length, \(L\), and radius, \(r\), we can use Gauss’ Law to determine the field at a distance, \(r\), from the wire: \[\begin{aligned} \oint \vec E\cdot d\vec A&=\frac...By using a cylindrical surface of length, \(L\), and radius, \(r\), we can use Gauss’ Law to determine the field at a distance, \(r\), from the wire: \[\begin{aligned} \oint \vec E\cdot d\vec A&=\frac{Q^{enc}}{\epsilon_0}\\ 2\pi r L E&= \frac{\lambda L}{\epsilon_0}\\ \therefore \vec E(r)&=\frac{\lambda}{2\pi\epsilon_0 r}\hat r\end{aligned}\] Using the electric field, we can calculate the potential difference between two points that are at distances, \(r_A\) and \(r_B\), from the wire: \[\begin{…
