  A new derivation of surface charges for 3+1 gravity coupled to
Electromagnetism is obtained. Gravity theory is written in the
tetrad-connection variables. The general derivation starts from the Lagrangian
and uses the covariant symplectic formalism in the language of forms. For gauge
theories surface charges disentangle physical from gauge symmetries through the
use of Noether identities and the exactness symmetry condition. The surface
charges are quasilocal, explicitly coordinate independent, gauge invariant, and
background independent. For a black hole family solution the surface charge
conservation implies the first law of black hole mechanics. As a check we show
the first law for black hole electrically charged, rotating, and with an
asymptotically constant curvature (the Kerr-Newman (anti-)de Sitter family).
The charges, including the would-be mass term appearing in the first law, are
quasilocal. It is not required a reference to the asymptotic structure of the
spacetime nor boundary conditions, and therefore topological terms do not play
a r\^ole. Finally, surface charges formulae for Lovelock gravity coupled to
Electromagnetism are exhibited. It generalizes the one derived in a recent work
by G. Barnich, P. Mao, and R. Ruzziconi. The two different symplectic methods
to define surface charges are compared and shown equivalent.
