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The balloon sticks to the wall due to the process of induction. When the balloon is brought closer to the wall, the negative charges in the wall are repelled by the negative charges on the balloon. This causes the negative charges in the wall to move away from the balloon, creating a positive charge on the surface of the wall closest to the balloon.
Opposite charges attract each other, so the positive charges on the wall are attracted to the negative charges on the balloon. This attraction is what causes the balloon to stick to the wall.