  The prominence of nulls in reconnection theory is due to the expected
singular current density and the indeterminacy of field-lines at a magnetic
null. Electron inertia changes the implications of both features. Magnetic
field lines are distinguishable only when their distance of closest approach
exceeds a distance $\Delta_d$. Electron inertia ensures $\Delta_d\gtrsim
c/\omega_{pe}$. The lines that lie within a magnetic flux tube of radius
$\Delta_d$ at the place where the field strength $B$ is strongest are
fundamentally indistinguishable. If the tube, somewhere along its length,
encloses a point where $B=0$,vanishes, then distinguishable lines come no
closer to the null than $\approx (a^2c/\omega_{pe})^{1/3}$, where $a$ is a
characteristic spatial scale of the magnetic field. The behavior of the
magnetic field lines in the presence of nulls is studied for a dipole embedded
in a spatially constant magnetic field. In addition to the implications of
distinguishability, a constraint on the current density at a null is obtained,
and the time required for thin current sheets to arise is derived.
