## Thursday, April 19, 2012

### Daddy Loves Froggy

To the outside observer, it may seem that scientists hate frogs.  Perhaps it's true.  After all, they're green, slimy, and with a little salt they can enter zombie mode.  That's probably not enough to justify dissection, but perhaps it's enough to justify this:

Now, I know what you're thinking.  It's a frog.  Levitating.  In a magnetic field.  WTF?!?!

Frogs aren't normally magnetic.   However, frogs (and other living creatures) contain water, which is a diamagnetic material.1  Diamagnetic materials have this weird property that when you place them in a magnetic field, they turn into a magnet themselves.  The new magnet points in the opposite direction of the first magnet.  In this way, a diamagnetic material is like a magnet that always repels.  Normally, this effect is very weak, but NASA scientists have shown that if you have a very big magnetic field, you can generate a magnetic force that is large enough to lift everyday objects like frogs.2  Now you might wonder why NASA cares about levitating frogs...

 Fr-fr-frogs...in-in-in...spa-spa-spaaaaaacce!!!

In truth, they've levitated more than just frogs.  Their goal seems to be eventually levitating a human.  This, of course, would be one way to mimic the effects of zero gravity.  How large of a magnetic field would it take to lift a human?

According to Wikipedia, it takes about 16 Tesla of magnetic field to levitate a frog.  For comparison, an MRI machine, which can erase all your credit cards if they're in the same room, has a magnetic field of 3 Tesla.

Now the magnetic field serves two purposes.  First, it magnetizes our prospective astronaut.  The amount he gets magnetized will be roughly proportional to the magnitude of the magnetic field.  After magnetizing the astronaut, the magnetic field will then push him up with a force that depends on both its own value and the value of the astronaut's magnetization.  Since the field appears twice in the force we can say that the force is proportional to the field squared:

Force ~ (magnetic field)2.

A small frog might weigh 50 grams, which is roughly 1000 times smaller than a human.  To get 1000 times the upward force, you'd need a field that's 32 times bigger.  (You can see this by squaring 32 to get roughly 1000 times the force.)  For this reason, you'd need a field that's about 500 Tesla, which is like having 170 MRI machines.

[1] Other diamagnetic materials include gold, silver, copper, carbon dioxide, and bismuth.