plates between which the current is measured.
The theory of this subject has been worked out independently by Child37 and Rutherford38. 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.
The current i1 per square centimetre through the gas is constant for all values of x, and is given by
By Poisson’s equation
Then
Integrating
where A is a constant. Now A is equal to the value of
when x = 0. By making the ionization very intense,