Gary Edwards, a 58 year old male from Carleton Place, Ontario, Canada asks on February 7, 2002,Why do carrots spark when cooked in a microwave? Peel 1/2 a carrot, dice it into small pieces, put pieces in a pot and boil, drain and let cool. Put carrots on a plate and place them in the microwave on high for thirty seconds, they spark - why? Does it have something to do with the sugar content?
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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.
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