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I just took a flannel shirt off and it crackled with static. I threw it on a metal chair and I hear it crackle some more. I played with a stray string with my hand, watching it rise to meet my hand and fall when I move it away. But this leaves me with a question to which I cant find an answer on Google. I know later I will pick up the shirt and the static will be gone. Where does static electricity go if its not grounded? Does it dissipate into the air? Or into the object its on?

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The charges on your shirt will disappear due to discharging through the small conductivity of air and the conductivity of the object where you have put your shirt on.

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Where does static electricity go if its not grounded?

Actually the floor (the earth) works as the ground: the electrons accumulated in the shirt will flow from the shirt to the chair and to the floor. Would the chair be on a rubber surface and the chair wouldn't discharge.

P.S.: The small conductivity of the air will also help the discharge (as pointed by @freecharly) but it's mostly via direct contact of the chair and floor.

P.P.S.: The reason why electric charge builds up when you go outside (during winter) is because most of the time you wear boots which provides an insulating layer between the floor and your body.

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