If I is the current through unit area of the gas and if we neglect any diffusion except that caused by the electric field,
n1ek1X + n2ek2X = I (2).
From equations (1) and (2) we have
| n1e = | 1 | ( | I | + | k2 | dX | ) (3), | |
| k1 + k2 | X | 4π | dx |
| n1e = | 1 | ( | I | - | k2 | dX | ) (4), | |
| k1 + k2 | X | 4π | dx |
and from these equations we can, if we know the distribution of electric intensity between the plates, calculate the number of positive and negative ions.
In a steady state the number of positive and negative ions in unit volume at a given place remains constant, hence neglecting the loss by diffusion, we have
| d | (k1n1X) = q − αn1n2 (5). |
| dx |
| - | d | (k2n2X) = q − αn1n2 (6). |
| dx |
If k1 and k2 are constant, we have from (1), (5) and (6)