  We measure the penetration depth $\lambda_{ab}(T)$ in
Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$ using local techniques that do not average
over the sample. The superfluid density $\rho_s(T)\equiv1/\lambda_{ab}(T)^2$
has three main features. First, $\rho_s(T=0)$ falls sharply on the underdoped
side of the dome. Second, $\lambda_{ab}(T)$ is flat at low $T$ at optimal
doping, indicating fully gapped superconductivity, but varies more strongly in
underdoped and overdoped samples, consistent with either a power law or a small
second gap. Third, $\rho_s(T)$ varies steeply near $T_c$ for optimal and
underdoping. These observations are consistent with an interplay between
magnetic and superconducting phases.
