the value of
can be made extremely small.
Putting A = 0, we see that
This gives the potential gradient between the plates for different values of x.
Integrating between the limits 0 and d,
or
If i2 is the value of the current when the electric field is reversed, and K2 the velocity of the negative ion,
and
The current in the two directions is thus directly proportional to the velocities of the positive and negative ions. The current should vary directly as the square of the potential difference applied, and inversely as the cube of the distance between the plates.
The theoretical condition of surface ionization cannot be fulfilled by the ionization due to active substances, as the ionization extends some centimetres from the