The electric force on an ion is F_e = qE. Assuming Stokes' law for the viscous drag force in a solution, F_d = 6πηRv, where η is viscosity, R is the ion's radius, and v is its drift velocity. In steady state, F_e = F_d, so qE = 6πηRv. The drift velocity is v = qE / (6πηR). The ionic current I is proportional to the charge of each ion (q), the number density of ions (n), their drift velocity (v), and the cross-sectional area (A): I = nqvA.
Ions in a solution are subject to a uniform electric field. If each ion carries charge q and has radius R, then the ionic current I due to the applied field will depend on q and R as :
Asked in UPSC Geoscientist 2024 · Topic: Electric Current (Drift velocity and microscopic origin of current)
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