Sparks in Air

The phenomenon of an electric field causing air to ionize such that the air emits light and sound is known as a spark. Sparks occur between two opposing charges, where the electric field between them is strong enough to cause the air molecules to split from their normally stable state, into positive and negative ions that can conduct current.

The Physical Model

At a high level of abstraction, the occurrence of a spark is marked by three phases: the ionization of air particles, the propagation of the electric field in the air gap, and the neutralization of charges due to cancellation. These are no finite boundaries between these phases, although there is a general order to them, despite how quickly a spark occurs.

Ionization of Air

In air, there is always some chance occurrence of ionized particles. However, air molecules (most notably Nitrogen and Oxygen) are very stable, so these ions do not make up a significant portion of all air molecules in our atmosphere. These stable molecules require a relatively large amount of energy to separate them from their electrons. Typically, collisions between air particles do not impart enough energy to ionize them -- separate them from some of their electrons.

However, in the presence of a strong electric field, chance ions in the accelerate to very high speeds, gaining relatively large amounts of kinetic energy. In a strong enough electric field, these ions gain enough Kinetic energy to break apart air molecules when upon collision. The separation of the electrons from these air molecules creates two more ions: one negative (the electron) and one positive (the N2+ or O2+)

Propagation of the Electric Field

Because electric fields are strongest near each of the two opposite charges, the chain reaction of ionization starts there. The new ions created through collisions with the ions accelerated by the electric field also accelerate due to the electric field. These new ions can then cause more air particles to ionize by striking them at high speeds. The negatively charged ions move towards the positively charged object that started the spark, and the positively charged ions move towards the negatively charged object. As this happens, the charge distribution in the air between the two charged objects changes. Before the spark began, the electric field emanated from the two charged objects. As ions begin to form, the electric field also emanates in part from the ionized air. This causes the electric field between the two charged object to become more uniform, much like what occurs in a wire when a circuit is closed. Eventually, the chain reactions coming from each charged object meet in the middle, and the "circuit" is complete.

Neutralization of Charges

The molecules of the air are now sufficiently ionized to carry a current. The electrons in the gap move relatively rapidly toward the positively charged object, while the positive ions move very slowly towards the negatively charged object, due to the differences in their masses. As the ions hit the charged surfaces to which they are attracted, they combine with oppositely charged particles on that object's surface. When this happens, the charge on each object diminishes due to the cancellation of fields. Soon, there is no longer enough charge on the objects to accelerate the ions enough to maintain an ionized air gap. As the charged particles move through, the air, they are constantly recombining with other ions in the process of random motion, before being again knocked apart by an accelerated charge. Sparks produce light because when molecules recombine, they move to a lower energy state, and emit the difference in energy as a photon. These continual reactions produce a lot of heat, which cases the air gap to rapidly expand and make the sound we hear when a spark occurs.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.