A long wire has a linear charge density of 𝜆 = 3.8 𝜇C/m. What is the magnitude of the electric field from this wire at a distance of d = 45 cm from the wire?

Question

A long wire has a linear charge density of 𝜆 = 3.8 𝜇C/m. What is the magnitude of the electric field from this wire at a distance of d = 45 cm from the wire?

E =  __ N/C

Answer 1

By symmetry, the electric field E = Ee_r points in the radially transverse direction and is independent of axial coordinate z and azimuthal coordinate θ, so it depends only on transverse radius E = E(r). Imagine a cylinder of length L, radius d concentric with the wire, that therefore contains a charge λL. The volume integral of div E is the surface integral 2πdLE(r=d). Now apply the Gauss Law.