Problem — Lightning rod

Problem

Lightning rod. Explain why a pointed lightning rod protects a house, even though it does not “catch” every lightning strike. Discuss the role of surface charge density and air ionisation.

Solution

Dispersive power of points. On a conductor in equilibrium the charge distributes over the surface with a density $\sigma$ that is larger the smaller the radius of curvature: at points $\sigma$ is very high. Since the field just outside the conductor is

$E = \frac{\sigma}{\varepsilon_0}$

a point generates an extremely intense electric field in its immediate vicinity.

Air ionisation (corona effect). The high field at the point ionises the surrounding air, making it conductive. This creates a preferential channel that carries the discharge to earth: the point “draws off” and gently discharges the charges, reducing the likelihood of lightning and offering a low-resistance path to strikes that do occur.

Why not every strike. The lightning rod does not intercept every single lightning bolt: its function is to reduce the field around the building and provide the preferential point of impact and discharge path, thereby protecting the house by channelling most discharges to earth.

$\ev{\text{Punta} \Rightarrow \sigma \text{ grande} \Rightarrow E \text{ alto} \Rightarrow \text{ionizzazione e canale conduttivo verso terra}}$

Linked atoms

Topics: Elettrostatica Concepts: Conduttori in equilibrio elettrostatico · Campo elettrico