  The Breit equation with two electromagnetic form-factors is studied to obtain
a potential with finite size corrections. This potential with proton structure
effects includes apart from the standard Coulomb term, the Darwin term,
retarded potentials, spin-spin and spin-orbit interactions corresponding to the
fine and hyperfine structures in hydrogen atom. Analytical expressions for the
hyperfine potential with form factors and the subsequent energy levels
including the proton structure corrections are given using the dipole form of
the form factors. Numerical results are presented for the finite size
corrections in the 1S and 2S hyperfine splittings in the hydrogen atom, the
Sternheim observable $D_{21}$ and the 2S and 2P hyperfine splittings in muonic
hydrogen. Finally, a comparison with some other existing methods in literature
is presented.
