Fig. 9.
47. Variation of current with voltage for surface ionization.
Some very interesting results, giving the variation of the current with voltage, are observed when the ionization is intense, and confined to the space near the surface of one of two parallel plates between which the current is measured.
The theory of this subject has been worked out independently by Child[[80]] and Rutherford[[81]]. Let V be the potential difference between two parallel plates at a distance d apart. Suppose that the ionization is confined to a thin layer near the surface of the plate A (see [Fig. 1]) which is charged positively. When the electric field is acting, there is a distribution of positive ions between the plates A and B.
Let
n1
= number of positive ions per unit volume at a distance x from the plate A,
K1
= mobility of the positive ions,