Lightning Rod Field Enhancement · AI Generator #GEN-7EE72508

Physics · electromagnetism

Problem

During a thunderstorm, a tall lightning rod creates a region of enhanced electric field at its tip that helps initiate lightning strikes. Consider a simplified model where a lightning rod is approximated as a long conducting cylinder of radius

r = 2.0\;\text{cm}

carrying a surface charge density of

\sigma = 4.5 \times 10^{-6}\;\text{C/m}^2

. Just before a lightning strike, the electric field at the surface of the rod reaches the breakdown field strength of air,

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

. Using the given surface charge density, calculate the electric potential difference between the surface of the rod and a point

d = 15\;\text{cm}

away from the rod's surface (measured perpendicularly). You may treat the rod as infinitely long for this calculation.

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