Lightning Rod Safety Distance · AI Generator #GEN-C0439C4A

Physics · electromagnetism

Problem

A cylindrical lightning rod of height h=15  mh = 15\;\text{m} and radius r=2.0  cmr = 2.0\;\text{cm} is mounted on a flat roof. During a thunderstorm, the rod accumulates a charge of Q=8.0×10−6  CQ = 8.0 \times 10^{-6}\;\text{C} due to charge separation in the atmosphere. A maintenance worker on the roof needs to know the minimum safe distance from the base of the rod where the electric field strength drops to Esafe=1000  V/mE_{\text{safe}} = 1000\;\text{V/m} (below which air breakdown is unlikely). Treat the lightning rod as a uniformly charged conducting cylinder and assume the roof acts as an infinite grounding plane. For this configuration, the electric field at horizontal distance dd from the rod's base is approximately E=λ2πϵ0dE = \frac{\lambda}{2\pi\epsilon_0 d}, where λ\lambda is the linear charge density. Find the minimum safe distance dsafed_{\text{safe}}.

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