The charge on the balloon induces charges on the wall, in the same way that the metal object in Figure 2 becomes charged. A negatively charged balloon will induce a positive charge on the front surface of the wall, and a corresponding negative charge on its other side. The total charge on the wall will be zero, but, provided that the balloon remains charged, the charge on the wall will not redistribute. The balloon sticks to the oppositely-charged wall. QED.
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