Previous investigations on electrocapillary instability in a liquid me
tal confined in a circular cylindrical vessel are extended to annular
geometry. The number of peaks arising on an initially flat surface whe
n a strong electric field acts on it is determined in terms of the inn
er and outer ring radii, as well as the critical electric field needed
for destabilization. The limiting case of an infinite, straight recip
ient is independently solved and compared to the annular geometry resu
lts for appropriate values of these radii. Experimental observations w
ith mercury are included and confronted to the theory. (C) 1997 Americ
an Institute of Physics.