Electrical power lines are often not insulated, and the magnitude of the electric field of the surrounding air is about \(3 \times 10^{6} \mathrm{~N} / \mathrm{C}\). At greater electric field magnitudes, the air dissociates into charged particles, causing a breakdown and a big spark. You've been given a long sample of wire to test in the lab under electrostatic conditions, and you measure its diameter to be \(16.6 \mathrm{~mm}\). You have lots of equipment to produce a uniform linear charge density on the wire sample, and you figure you'd better build in a safety factor of 3 to account for humid days and so forth. What maximum charge density is safe?