[Arbitrary shapes of magnetic fields][1] are not possible, but [divergenceless][2] magnetic fields are physical. Various shapes of magnetic fields can be created by passing various, time dependent currents through a group of adjacent solenoids, but the use of solenoids imposes a significant limitation on spatial resolution of the created magnetic field. 

Is there a way to generate time variable magnetic fields with high spatial resolution? Can it be done without solenoids? Without moving parts?

  [1]: https://physics.stackexchange.com/questions/155553/is-it-possible-to-create-arbitrary-shapes-of-magnetic-fields
  [2]: https://en.wikipedia.org/wiki/Solenoidal_vector_field