Both “types” of electricity happen because of small negatively-charged particles called electrons. Because electrons are all negative, they’re constantly trying to get away from each other and get to something positively-charged. Positive charges are caused by protons, which are found in the center of every atom. The center of an atom, called the nucleus, usually has electrons orbiting it because they’re attracted to the positive protons. When an atom has the same amount of protons and electrons, we say it’s neutral. If the atom has too many electrons we call it negative, and if it doesn’t have enough we call it positive. Electrons are constantly moving around, which eventually can give us electricity.
With normal electricity, we “push” electrons through metal using batteries or generators using their attraction to positive charges. Solid metal is special because electrons can flow freely between atoms without orbiting them forever, which lets us have the “regular” electricity we use to power things.
With static electricity, (as an example) rubbing the atoms of your sleeve against the atoms of a rug causes your electrons to get shoved around, and your sleeve ends up with too many electrons. Your sleeve doesn’t let electrons move around much, so they get stuck and your sleeve becomes negatively charged. Since electrons dislike being next to each other, when you grab a door knob or someone’s hand, all those electrons see an opening to get away from each other, and they jump onto that more positive object, causing static shock.
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