First of all, our apologies for taking 2 years to answer your question. We're trying to periodically look through the deep backlog of submissions and we came across this.
You are right--Neutron stars, which are the densest stars that we believe are physically possible, tend to have extremely strong magnetic fields. You are also right, however, that you would be "mushed to a pulp" were you ever on the surface of one. You would be mushed into a pulp whose volume was about the same as a grain of sand
. "Mushed" meaning every atom which made up your body would be compressed into neutron degenerate matter and you would become part of the neutron star.
Curiously, adding more matter to a heavy neutron star actually makes it smaller
in size because the extra gravitational attraction of the extra mass is strong enough to squash the quantum neutron matter more than enough to make up for the added material. You could see that this could lead to trouble at some point. With too much matter, a neutron star becomes unstable, collapsing to a black hole.
Enough about gravity--you asked about its magnetic field. The magnetic field is indeed about a trillion times the strength of Earth's magnetic field. If you held a compass that somehow didn't weigh anything and therefore wasn't affected by the gravitational field of the neutron star, not only would it "fly out of your hands," the magnet would fly out of the compass itself
and probably disintegrate in the process because it would be different parts of the magnets will be accelerating at different rates. If the neutron star has a "dipole" magnetic field (the kind we have on Earth with a "North" and "South" pole), the particles would channel along the field lines to the poles.
I hope that answers some of your questions and our apologies for being so late!
(published on 05/09/11)