Through any cross-section between the electrodes and at right angles to the direction of motion of the ions, currents pass in the electrolyte of
I+ = en+v+, I_ = en_v_,
where e is the ion charge, n+ and n_ are the concentrations of the respective ions and v+ and v_ are their velocities.
The full current is
I = I+ + I_ = e(n+v+ + n_v_).
When n_v_ negative ions escape, the same number of positive ions remain near the cathode and they, together with the n+v+ positive ions which come to the cathode, are deposited there. Thus the number of positive ions deposited at the cathode is determined by the full current.
The position at the anode is similar.