  Q ball solutions are considered within the theory of a complex scalar field
with a gauged
  U(1) symmetry and a parabolic-type potential. In the thin-walled limit, we
show explicitly that there is a maximum size for these objects because of the
repulsive Coulomb force. The size of Q ball will increase with the decrease of
local minimum of the potential. And when the two minima degenerate, the energy
stored within the surface of the Q ball becomes significant.
  Furthermore, we find an analytic expression for gauged Q ball, which is
beyond the conventional thin-walled limit.
