From Coe College Chemistry website in Cedar Rapids, Iowa: "There is no ready explanation for this phenomenon in the physics or chemical literature. There may be a correlation among the dielectric constant, sample size and shape, moisture content for different foods, and the amount of sparking that takes place in the microwave field. In addition, the phenomenon can be modeled using salt solutions to mimic those present in a typical fruit or vegetable cell. Anecdotal evidence suggests that a cut edge of the fruit or vegetable must be present, touching that of another cut edge, for the phenomenon to occur. This phenomenon seems similar to that of the 'edge effect' where electrons congregate at the sharp edges and point of a metal in an electric field and can discharge via a spark to another edge or point nearby."

So this appears to be an area of research that is wide open. Another answer with frozen carrots appears at the New Scientist website in England.