Magnetic nulls in interacting dipolar fields

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 $\varDelta _d$. Electron inertia ensures $\varDelta _d\gtrsim c/ω _{pe}$. The lines that lie within a magnetic flux tube of radius $\varDelta _d$ 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 $≈ (a^2c/ω _{pe})^{1/3}$, where $a$ is a characteristic spatial scale of the magnetic field. The behaviour 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.