The Lightning Rod's Electric Shadow · AI Generator #GEN-F4FA47BA

Physics · electromagnetism

Problem

A tall lightning rod creates a "shadow zone" where the electric field is significantly reduced during thunderstorms. To model this effect, consider a long conducting rod of radius R=2.0  cmR = 2.0\;\text{cm} that extends vertically from the ground. During a storm, there is a uniform horizontal electric field E0=1.2×105  V/mE_0 = 1.2 \times 10^5\;\text{V/m} in the surrounding air. Due to the conducting rod, the electric field is distorted, and at a horizontal distance d=50  cmd = 50\;\text{cm} from the rod's center, the electric field magnitude is reduced to E=8.0×104  V/mE = 8.0 \times 10^4\;\text{V/m}. Assuming the rod can be modeled as an infinitely long conducting cylinder, what is the electric potential difference between a point at distance dd from the rod and a point at distance 2d2d from the rod, both measured horizontally from the rod's center?

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