  We consider the coulomb gas model on the upper half plane with different
boundary conditions, namely Drichlet, Neuman and mixed. We related this model
to SLE($\kappa,\rho$) theories. We derive a set of conditions connecting the
total charge of the coulomb gas, the boundary charges, the parameters $\kappa$
and $\rho$. Also we study a free fermion theory in presence of a boundary and
show with the same methods that it would lead to logarithmic boundary changing
operators.
