Ok, most people including me know that formal charge is just a book-keeping tool. I know how to calculate it, apply it to Lewis structures etc etc. But I am confused in its very basic definition which says - "Formal charge is the charge on an atom if the electronegativity differences are ignored" . If the electronegativity difference is ignored, then how can an atom have charge ? I know this is not a place to ask such a basic question , but still I am very confused about this miniscule definition.
A good description appears in the book, "Chemistry A Molecular Approach".
In the molecule of hydrogen fluoride, we know that it has a dipole moment, and fluoride is slightly negative. Ignoring this information (electronegativity difference) and we share the bonding electrons equally, the formal charge can be calculated, and both of them are determined to be 0.
In reality, we know that fluoride has the electron from the hydrogen most of the time (due to electronegativity difference). We say the hydrogen has a partial positive charge and the fluoride has a partial negative charge.
From this, it is apparent that the formal charge is different from the charge on the atoms in a molecule.
The formal charge is the charge on an "ion" that results when all valence electrons participating in bonds are assumed equally shared between this "ion" and the others it is bonded to. If we consider, for example, nitrogen bonded to three carbon atoms using its 3 bonding electrons then it loses, assuming equal sharing, 1/2 an electron to each carbon but gets back a half share in an electron from each carbon. Net charge on the nitrogen: 0. Now assume that the unshared pair form a second bond with one of the carbons. The nitrogen loses a half share in each of those two electrons but does not get back a half share from the carbon in this case. Thus the nitrogen has a formal charge of +1. But this is a formal charge. A bookkeeping convenience - nothing more. In actuality the electronegativities of carbon and nitrogen will determine where the electrons spend their time and thus the apparent charge distribution. Obviously it would be quite tedious to try to figure out what those charge distributions would be. It's handy sometimes to assume, when considering covalent bonds, that they are perfectly covalent.
It's best to think about why electronegativity is used in this definition of formal charge and perhaps replace it with a concept that is familiar. One definition of electronegativity is the ability of an atom to attract electron density towards itself. So if we think of a simple diatomic series with (lewis pairs added) like: H:H, H:Br, H:Cl and H:F, with electronegativities H < Br < Cl < F, then those two electrons ":" are closer to F than they are to Cl, which in turn are closer to the Br atom and in H:H they are shared equally. Now the formal charge is the number of electrons ascribed to the atom minus the atomic number. So the question is how do we ascribe an electron to each atom? If we try to include electronegativity arguments then we would ascribe more electrons to F then to Cl in those diatomics and the formal charges in HF and HCl would be different. However, if we ignore the electronegativity and let the atoms share the electrons equally (like in a lewis diagram) then we arrive at the familiar formal charge definition that you have noted.