  We address the problem of controllability of the MHD system in a rectangular
domain with a control prescribed on the side boundary. We identify a necessary
and sufficient condition on the data to be null controllable, i.e., can be
driven to the zero state. We also show that the validity of this condition
allows the states to be stirred to each other. If the condition is not
satisfied, one can move from one state to another with the help of a simple
shear external magnetic force.
