## Wednesday, February 1, 2012

### Alton Brown Wants to Burn Your House Down

I'm a big fan of Food Network's resident gastrophysicist, Alton Brown.  Mr. Brown excels at explaining food science to lay people in fun and entertaining ways.  With this in mind, I'm kind of sad to call him out on an egregious error in one of his recipes.  The recipe, "Plain Brown Popper", gives the following instructions:

"Toss the popcorn with the olive oil, salt, and jalapeno seasoning mix in the paper bag. Fold the top of the bag over and staple the bag twice to close. Place the bag in the microwave and microwave on high for 2 minutes to 3 minutes..."

Come again?  Staple?!  As in a metal staple?  In a microwave?! Perhaps staples are too small to do any damage.  How bad is it to put a metal staple in a microwave?

Microwaves work by generating an oscillating electric field that vibrates the electrically polarized water molecules inside.  Humans observe this enhanced molecular movement as an increase in the temperature of the food.  However, water molecules aren't the only things that are getting pushed by the electric field.  Any mobile electric charges will vibrate as well, including the electrons in any conductive metal that found its way into the microwave.  Charges in the metal can move around in  a way that will make the electric field even bigger.  If the field is large enough (~3×106 V/m), sparking will occur, which can start a fire.

If there's any electric field inside a metal, it will push the electrons from one side of the metal to the other.  In fact, the field will keep pushing electrons from one side to the other until the electric field created by these electrons exactly cancels out the original field.  This happens very quickly because electrons move very fast.  Electrons cancel out the electric field in metals so quickly that we can often assume the electric field inside a conductor is always zero.  How many electrons would it take to cancel out the 2×103 V/m field created by many microwaves?  Well, if you take a plate and put charge on the opposite faces, you'll find the charge on a surface is given by

total charge = (permittivity of space) · (electric field) · (area),

where the "permittivity of space" is a constant equal to 8.854×10-12 F/m.  Plugging in 0.5 mm by 1 cm for the area, you get a total charge

total charge = ( 8.854×10-12 F/m) · (2×103 V/m) · (0.5 mm × 1 cm)
= 1×10-14 C.

That's a small charge, and it doesn't create much of an electric field when spread out over broad side of a staple.  However, when the same charge aggregates on the sharp end of the staple, the electric fields can get quite large because the area is so small.  If sharpened, the points might have and area of 0.05 mm by 0.05 mm,

electric field = (total charge) / [ (permittivity of space) · (area) ],
= (1×10-14 C) / [ ( 8.854×10-12 F/m) · (0.05 mm × 0.05 mm) ],
= 4×106 V/m

That's more than large enough to generate a spark. The electric field just outside the staple will depend greatly on how sharp the surface is, with sharper objects being more likely to spark.  With the possible exception of pets and small children, a staple might be the worst of all possible things to put in a microwave.1,2,3

[1] Being a scientist, I had to test whether or not putting staples in a microwave was actually harmful.  Mr. Brown, you owe me one microwave.
[2] Special thanks to Melinda Keller, who directed me to a very nice article in The Physics Teacher titled "Microwave Mischief and Madness", by Heather Hosack, Nathan Marler, and Dan MacIsaac.
[3] Immediately after posting this, I was struck by the realization that the quasi-static approximation I've made might not be legit.  I think I'm right on this (my microwave was incinerated after all), but feel free to call me out on it if I'm making a mistake.