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The proton motive force arises from a combination of the concentration gradient of protons and a voltage gradient across the membrane (the protons are positively charged, so an imbalance of protons means that the side of the membrane with more protons has a positive charge relative to the side with fewer protons).
The result is that protons quite strongly 'want' to cross the membrane from the right to the left, both to even out concentrations and to even out charges. The overall process of ATP generation via the harnessing of a proton motive force is called chemiosmosis.