The balloon sticks to the wall due to the phenomenon of electrostatic induction. Here's how it works:
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Charge Separation: When you rub a balloon on your hair or a similar material, it becomes negatively charged due to the transfer of electrons. When you bring this negatively charged balloon close to a neutral wall, the negative charge on the balloon repels the electrons in the wall's surface.
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Induced Positive Charge: This repulsion causes the electrons in the wall to move away from the side closest to the balloon, leaving that side with a slight positive charge. The wall remains overall electrically neutral, but there is a charge separation occurring.
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Attraction: The negative charge on the balloon is now attracted to the induced positive charge on the wall. This attractive force between the negatively charged balloon and the positively charged area of the wall causes the balloon to stick.
In summary, the attraction between the charged balloon and the induced positive charge on the wall, despite the wall remaining overall neutral, is what causes the balloon to adhere to the wall.