  Magnetic fields likely play a key role in the dynamics and evolution of
protoplanetary discs. They have the potential to efficiently transport angular
momentum by MHD turbulence or via the magnetocentrifugal acceleration of
outflows from the disk surface, and magnetically-driven mixing has implications
for disk chemistry and evolution of the grain population. However, the weak
ionisation of protoplanetary discs means that magnetic fields may not be able
to effectively couple to the matter. I present calculations of the ionisation
equilibrium and magnetic diffusivity as a function of height from the disk
midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling
by soaking up electrons and ions from the gas phase and reducing the
conductivity of the gas by many orders of magnitude. However, once grains have
grown to a few microns in size their effect starts to wane and magnetic fields
can begin to couple to the gas even at the disk midplane. Because ions are
generally decoupled from the magnetic field by neutral collisions while
electrons are not, the Hall effect tends to dominate the diffusion of the
magnetic field when it is able to partially couple to the gas.
  For a standard population of 0.1 micron grains the active surface layers have
a combined column of about 2 g/cm^2 at 1 AU; by the time grains have aggregated
to 3 microns the active surface density is 80 g/cm^2. In the absence of grains,
x-rays maintain magnetic coupling to 10% of the disk material at 1 AU (150
g/cm^2). At 5 AU the entire disk thickness becomes active once grains have
aggregated to 1 micron in size.
