In this case practically all the current is carried by the negative ions so that i = n2k2Xe, and therefore q = αn1n2.
Thus
n2 = i/k2Xe, n1 = qk2Xe/αi.
Thus
| dX | = | 4πe²k2qX | - | 4πi | , |
| dx | αi | k2X |
or
| dX² | - | 8πe²k2qX² | = - | 8πi | . |
| dx | αi | k2 |
The solution of this equation is
| X² = | α | i² | + Cε 8πe² k2qx/αi. | |
| q | k²2e² |
Here x is measured from the positive electrode; it is more convenient in this case, however, to measure it from the negative electrode. If x be the distance from the negative electrode at which the electric force is X, we have from equation (7)