Yes, according to the Parker Dynamo Model developed in the 1960's.
Magnetic fields are generated by circulating currents of charged particles in a medium that is electrically-conducting. The sun represents a rotating gaseous body of high-temperature plasma with one type of conductivity. The Earth rotates much faster, and the liquid iron-nickel in its core has another conductivity. Jupiter rotates even faster and has yet another type of conductive core region. Parker described how the fields are generated, and derived a simple formula that describes the strength of the field AND how rapidly the field would reverse its polarity. For the sun, with some reasonable estimates for its conductivity and rotation speed, you get a polarity reversal time of about 20-50 years. For the earth, this number is between 200,000 and 500,000 years. In each case, the reversal period estimate matches pretty nearly what is actually determined from the sun spot record and from studies of terrestrial paleomagnetism. There are, however, some detailed problems with Parker's model for solar activity, but it is still the simplest one we have to go with for purposes of classroom instruction.
All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the
NASA IMAGE/POETRY project.