Final answer:
Corona discharges occur around sharp points on charged metal objects because these points have a high concentration of charge, leading to very strong electric fields. When the electric field exceeds about 3.0 × 10^6 N/C, it ionizes the air molecules, resulting in corona discharge. Lightning rods utilize this principle to safely dissipate excess charge.
Step-by-step explanation:
A corona discharge can occur when there is a strong electric field around a sharp point on an electrically charged metal object. This is because the surface charge density and the electric field of a conductor are greater at regions with smaller radii of curvature. This implies that any excess charge on a conductive object tends to collect at sharp points or corners, creating a very high concentration of charge at those points. Furthermore, as electric fields are vectors that point from positive to negative charges, they become stronger where these charges are more concentrated. Specifically, the electric field around a sharp point on a conductor becomes very strong, which can exert a force large enough to remove or transfer charge on or off the conductor. For instance, when the electric field reaches a value of approximately 3.0 × 106 N/C (the dielectric strength of the air), it can ionize surrounding air molecules, resulting in a corona discharge. This concept is harnessed in devices such as lightning rods, which prevent the buildup of large excess charges on structures by directing charges into the Earth, thus avoiding damaging electrical discharges.