A gas is ionized in the immeiate vicinity of the surface of plane electrode `I` (Fig) separated from electrodes 2 by a distanae `l`. An alternating voltage varying with time `t` as `V = V_(0) sin omega t` is applie dto the electrodes. On decreasing the frequency `omega` it was observed that the galvonometer `G` indicates a current only at `omega lt omega_(0)`, where `omega_(0)` is a certain cut-off frequency. FInd the mobility of ions reaching electrode 2 under these conditions.

Explanation

Velocity = mobility `xx` field
or, `v = u (V_(0))/(l) sin omega t`, which is positive for `0 le omega t le pi`
So, maximum displacement in one direction is
`x_(max) = int_(0)^(pi) u (V_(0))/(l) sin omega t dt = (2 u V_(0))/(l omega)`
At `omega = omega_(0), x_(max) = l`, so `(2u V_(0))/(l omega) = l`
Thus `u = (omega l^(2))/(2 V_(0))`