Electrical resistivity and conductivity results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma ("n" = <Z>"n"), but on the scale of the Debye length there can be charge imbalance. In the special case that "double layers" are formed, the charge separation can extend some tens of Debye lengths. The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation: Differentiating this
Negative number the rules of signs for expanding the multiplication formula_3, and al-Karaji wrote in his "al-Fakhrī" that "negative quantities must be counted as terms". In the 10th century, Abū al-Wafā' al-Būzjānī considered debts as negative numbers in "A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen". By the 12th century, al-Karaji's successors were to state the general rules of signs and use them to solve polynomial divisions. As al-Samaw'al writes: the product of a negative number — "al-nāqiṣ" — by a positive number — "al-zāʾid" — is negative, and by a negative number is positive.