Why does the door bell ring when it does?

The sharp ring of the doorbell is used to increase the tension and as an abrupt prelude to the inspector's arrival. It also represents the contrast of two political ideologies. Birling is in the middle of his speech expounding the virtues of Capitalism when the door-bell rings. The inspector, on the other hand will introduce a more socialist ideology that "everybody has to look after everybody else." Priestly uses the doorbell to signal dramatic tension between opposing political value systems.