  This paper considers the possibility that two charged particles with an
attractive short-ranged potential between them which is not strong enough to
form bound states in free space, may bind in uniform magnetic fields. It is
shown that in the formal limit where Coulomb repulsion is negligible (q -> 0
and B_0 -> \infty with q B_0 fixed where q is the charge and B_0 the field
strength) there always exists a bound state for a system of two identical
charged particles in a constant magnetic field, provided that there is a
short-range uniformly attractive potential between them. Moreover, it is shown
that in this limit {\it any} potential with an attractive s-wave scattering
length will posses bound states provided that the range of the potential is
much smaller than the characteristic magnetic length, r_0 = (\frac{q
B_0}{4})^{-1/2}. For this case, the binding is computed numerically. We
estimate the size of the magnetic field needed to approximately reach a regime
where the formal limit considered becomes a good approximation to the dynamics.
These numerical estimates indicate that two protons in an extremely strong
magnetic field such as might be found in a magnetar will bind to form a
diproton.
