  Field emission studies incorporating the effect of space charge reveal that
for planar emitters, the steady-state field $E_P$, after initial transients,
settles down to a value lower than the vacuum field $E_L$. The ratio $\vartheta
= E_P/E_L$ is a measure of the severity of space charge effect with $\vartheta
= 0$ being most severe and $\vartheta \simeq 1$ denoting the lack of
significant effect. While, $E_L$ can be determined from a single numerical
evaluation of the Laplace equation, $E_P$ is largely an unknown quantity whose
value can be approximately found using physical models or can be determined
`exactly' by particle-in-cell or molecular dynamics codes. We propose here a
simple model that applies to planar as well as curved emitters based on an
application of Gauss's law. The model is then refined using simple
approximations for the magnitude of the anode field and the spread of the beam
when it reaches the anode. The predictions are compared with existing molecular
dynamics results for the planar case and particle-in-cell simulation results
using PASUPAT for curved emitters. In both cases, the agreement is good. The
method may also be applied to large area field emitters if the individual
enhancement factors are known, for instance, using the hybrid model (D.Biswas,
J. Vac. Sci. Technol. B 38, 063201 (2020)).
