  Using the Cottingham formula, we give an estimate of the electromagnetic mass
splitting of pseudoscalar heavy mesons in the beauty and charm sector. We
include in the dispersion relation the Born term, the $1^-$ resonance and the
positive parity $1^+$ resonance. We also evaluate the contribution to the mass
difference from the isospin breaking quark mass differences. Our results:
$m_{B^+}-m_{B^0} = - 0.83\pm 0.34 MeV$ and $m_{D^+}-m_{D^0} = + 4.33\pm 0.37
MeV$, are in agreement with the experimental measurements: $m_{B^+}-m_{B^0} = -
0.35\pm 0.29 MeV$ and $m_{D^+}-m_{D^0} = + 4.78\pm 0.10 MeV$. We also compute
the mass differences in the infinite heavy quark mass limit, which show small
deviations from the finite mass results for the B case and 30% effects in the
charm case.
