  The field enhancement factor at the emitter tip and its variation in a close
neighbourhood determines the emitter current in a Fowler-Nordheim like
formulation. For an axially symmetric emitter with a smooth tip, it is shown
that the variation can be accounted by a $\cos{\tilde{\theta}}$ factor in
appropriately defined normalized co-ordinates. This is shown analytically for a
hemi-ellipsoidal emitter and confirmed numerically for other emitter shapes
with locally quadratic tips.
