The Lightning Rod's Electric Shadow · AI Generator #GEN-91E82BD9
Physics · electromagnetism
Problem
A tall lightning rod creates a "shadow" region below storm clouds where the electric field is significantly reduced. Consider a simplified model where a storm cloud creates a uniform downward electric field of magnitude E0=2.5×104N/C over a large area. A conducting lightning rod of height h=25m and negligible thickness is placed vertically on the ground. Due to the rod's presence, the electric field is reduced to zero at a point on the ground directly below the storm cloud, located a horizontal distance d=15m from the base of the lightning rod. Assuming the ground acts as a perfect conductor, find the magnitude of the induced charge per unit length on the lightning rod.