Final answer:
The standing out of hairs is caused by static electricity, where an imbalance of electrical charge results in excess positive charges that repel each other, making the hairs stand apart.
Step-by-step explanation:
The hairs of Bill Nye's "Rocking Wig of Science" stand out as they do primarily due to static electricity. Much like the way a child's hair stands on end after going down a plastic slide, or how someone's hair reacts when touching a Van de Graaff generator, the underlying principle involves the transfer of electrons which creates an excess of positive charges. These positive charges repel each other, causing each strand of hair to similarly repel its neighbors and stand up.
Most objects don't exhibit static electric effects in everyday circumstances because the charges are typically balanced; however, certain actions can strip electrons away, resulting in an imbalance and the visible effects of static electricity. Therefore, while synthetic fibers, magnetic fields, and stylistic choices may affect the appearance of hair or a wig, it's the excess of positive charges from static electricity that is responsible for the distinct hair-raising effect seen in the scenarios described.