How Do Ions Respond to the Electric Field

In the absence of an electric field, ions are in ceaseless random motion. This random walk of ions has been shown to have an important characteristic The mean distance traversed by the ions as a whole is zero because while some are displaced in one direction, an equal number are displaced in the opposite direction. From a phenomenological view, therefore, the random walk of ions can be ignored because it does not lead to any net transport of matter (as long as there is no difference in 

Under the influence of an electric field, however, the net result of the zigzag jumping of ions is not zero. Ions feel the electric field i.e., they experience a force directing them toward the electrode that is charged oppositely to the charge on the ion. 

This directed force is equal to the charge on the ion, times the field at the point where the ion is situated. The driving force of the electric field produces in all ions of a particular species a velocity component in the direction p of the potential gradient. Thus, the establishment of a potential difference between the electrodes produces a drift, or flux, of ions (Fig. 4.47). This drift is the migration (or conduction) of ions in response to an electric field. 

As in diffusion, the relationship between the steady-state flux J of ions and the driving force of the electric field will be represented by the expression 

For small fields, the terms higher than BX will tend to zero. Further, the constant A must be zero because the flux of ions must vanish when the field is zero. Hence, for small fields, the flux of ions is proportional to the field (see Section 4.2.2) 

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