  Mutual sticking of dust aggregates is the first step toward planetesimal
formation in protoplanetary disks. In spite that the electric charging of dust
particles is well recognized in some contexts, it has been largely ignored in
the current modeling of dust coagulation. In this study, we present a general
analysis of the dust charge state in protoplanetary disks, and then demonstrate
how the electric charging could dramatically change the currently accepted
scenario of dust coagulation. First, we describe a new semianalytical method to
calculate the dust charge state and gas ionization state self-consistently.
This method is far more efficient than previous numerical methods, and provides
a general and clear description of the charge state of gas-dust mixture.
Second, we apply this analysis to early evolutionary stages where the dust has
been thought to grow into fractal ($D \sim 2$) aggregates with a
quasi-monodisperse (i.e., narrow) size distribution. We find that, for a wide
range of model parameters, the fractal growth is strongly inhibited by the
electric repulsion between colliding aggregates and eventually "freezes out" on
its way to the subsequent growth stage involving collisional compression.
Strong disk turbulence would help the aggregates to overcome this growth
barrier, but then it would cause catastrophic collisional fragmentation in
later growth stages. These facts suggest that the combination of electric
repulsion and collisional fragmentation would impose a serious limitation on
dust growth in protoplanetary disks. We propose a possible scenario of dust
evolution after the freeze-out. Finally, we point out that the fractal growth
of dust aggregates tends to maintain a low ionization degree and, as a result,
a large magnetorotationally stable region in the disk.
