Lightning Rod on a Skyscraper · AI Generator #GEN-B3CC1266

Physics · electromagnetism

Problem

A modern skyscraper has a copper lightning rod extending

h = 2.0\;\text{m}

above its flat roof. During a thunderstorm, the electric field in the air near the tip of the lightning rod reaches

E = 3.0 \times 10^6\;\text{V/m}

just before a lightning strike occurs. For the purposes of this calculation, model the lightning rod as a conducting cylinder with radius

r = 1.5\;\text{cm}

and assume the electric field is uniform and points vertically downward from a storm cloud that can be treated as an infinite conducting plane located far above the rod. The building's roof is grounded and can be considered to be at zero potential. What is the electric potential at the tip of the lightning rod just before the lightning strike?

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