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Induced dipole implies that before a heavily charged ion came near the original atom, the atom was nonpolar. Even though the atom was nonpolar, it has a cloud of electrons surrounding it. Putting a charged ion near the nonpolar atom disturbs the arrangement of the electrons so that the originally nonpolar atom becomes slightly charged in favor of being attracted to the charged ion.
The dipole-induced-dipole interaction is when a polar molecule interacts with a non polar molecule. This interaction arises from the ability of one molecule to induce a dipole moment in the other. However, in this case, the molecule that induces the dipole moment has a permanent dipole moment. The potential energy of there interaction is once again inversely proportional to the sixth power of the separation. In a dipole-induced dipole interaction, the polar molecule pulls the electron density of the non-polar molecule towards delta positive, fluctuating the electron distribution.
An induced dipole results from the interaction between a nonpolar molecule and another molecule, which can be very polar depending on the type of interaction. As the polar molecule moves closer to the non polar molecule, the distribution of charge in the polar molecule causes the arrangement of electrons in the originally nonpolar molecule to rearrange. Once the electrons are rearranged, the molecule is now considered a dipole because the charges within the molecule are separated. Therefore, an induced dipole is a nonpolar molecule that arranges itself into a dipole when it encounters a poler molecule. Here, I described a dipole-induced dipole interaction, but there are other types of interactions between molecules.
You can also get an induced dipole from a non dipole: this is the induced dipole - induced dipole interaction. The way I understand it is because electrons are really always moving around, there are times when some parts of a non-dipole molecules are partially charged in some areas, which can affect nearby molecules, and it becomes a positive feedback loop until both molecules have become induced dipoles.
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