The Lightning Rod's Electric Shadow · AI Generator #GEN-8AECA23B

Physics · electromagnetism

Problem

A lightning rod is modeled as a long, thin conducting cylinder of radius

a = 2.0\;\text{cm}

and height

h = 15\;\text{m}

, mounted vertically on a flat conducting ground plane. During a thunderstorm, the rod accumulates a total charge of

Q = +45\;\mu\text{C}

distributed uniformly along its length. A small test charge

q = -3.0\;\text{nC}

is placed at ground level at a horizontal distance

d = 8.0\;\text{m}

from the base of the rod. Since the rod is much longer than its radius (

h \gg a

), it can be treated as a line charge for points not too close to its ends. Find the magnitude of the electric force on the test charge.