| X1 = X0( | k1 | )1/2 | 1 | , | X2 = X0( | k2 | )1/2 | 1 | . |
| k2 | √ε | k1 | √ε |
Therefore
X1/X2 = k1/k2,
| Fig. 12. |
or the force at the positive plate is to that at the negative plate as the velocity of the positive ion is to that of the negative ion. Thus the force at the negative plate is greater than that at the positive. The falls of potential V1, V2 at the two layers when 1/ε is large can be shown to be given by the equations
| V1 = 8π²( | ε | )3/2k1( | k1 | )1/2i², |
| qα | k2 |
| V2 = 8π²( | ε | )3/2k2( | k2 | )1/2i², |
| qα | k1 |
hence
V1/V2 = k1²/k2²,
so that the potential falls at the electrodes are proportional to the squares of the velocities of the ions. The change in potential across the layers is proportional to the square of the current, while the potential change between the layers is proportional to the current, the total potential difference between the plates is the sum of these changes, hence the relation between V and i will be of the form