  The distribution of net electric charge in graphene is investigated, using
both a constitutive atomic charge-dipole interaction model and an approximate
analytical solution to Laplace's equation. We demonstrate a strong size
dependence of the charge distributions in finite-size, infinitely-long and
multi-layered rectangular graphene sheets, respectively. We found that the
charge density can be naturally enhanced up to 13 times at graphene's geometry
edges. This edge charge enhancement effect becomes more significant when the
length or the width of graphene increases. The charge enhancement ratio is
found to follow a linear relationship with the number of layers. These results
can be used to understand the newly experimentally observed electron emission,
charge impurity and chemical doping phenomena in 2-dimension nanostructure.
