The electric field along a magnetic neutral line of the O type can be estimated by method previously applied by Alfv¿n to neutral sheets, with the same result: the line integral of the electric field along the neutral line, multiplied by the elementary charge, is at most equal to twice the magnetic energy per particle. The same upper limit, within a numerical factor of order unity, is obtained from a hydromagnetic calculation where the plasma flow toward the O line is balanced by outflow within the narrow region where the hydromagnetic coupling between the flow and the electric field breaks down. The same upper limit can also be derived from nonsteady models with a nonzero curl of the electric field (no E¿B inflow) or with a nonzero divergence of the mass flux density (No outflow), as well as from a model that involves anomalous resistivity when the current density exceeds a threshold value. The derived upper limit implies that the maximum energy that is gained by a particle that drifts along the O line is not significantly greater than the typical energy of a plasma sheet particle; hence simple acceleration by electric fields along magnetic O lines cannot account for the energetic component of the charged particle population in the magnetotail.