The constant field couples with nuclear spin, forming new energy levels.  
Put a sample in a constant and in a varying magnetic field.  The constant field couples with nuclear spin, forming new energy levels.  The second field, usually radio waves, can have the frequency to excite transitions between the new states.  A transition tells about the sample's composition-- usually, the presence of hydrogen and carbon-13.  For ten points, name this type of spectroscopy, very similar to a medical scanning technique.
Put a sample in a constant and in a varying magnetic field.  
NMR or nuclear magnetic resonance