Saturday, February 21, 2009

Dr. Crazy nails it ...

I really love teaching undergraduates hard stuff.

That is what I love about my job.

There are some really challenging subjects in the physics course I teach, ones that challenged me when I first encountered them. Ideas that blend math and science, often math they have not learned yet, or are also encountering for the first time. Its great to see students "get it", especially when it seems like the entire class gets it.

The entertaining part is that my students may never know that the really sweet explanation I gave them of a trick for remembering a particularly nasty equation (the Biot-Savart Law, for any physicists reading this) was something I figured out for the very first time this semester! It probably came across to them as a detail that was just as practiced as something I have explained the same way every one of the dozens of times I have taught this course, if I did it well.


Tom said...

As a physics student, I think I can speak for all of us when I say, what was the really sweet trick for remembering Biot-Savart?

Doctor Pion said...

That was quick!

The starting point assumes you KNOW the following (pseudo-TeX used for the equations):

F = qE

E = (1/4*pi*epsilon) int{ dq r-hat / r^2 }

The latter is obvious from the Coulomb formula even if you don't use the integral form very often.

Think about starting from F and changing q to dq and putting r-hat where E is when constructing the numerator of the integrand for E.

You also KNOW the Lorentz force:

F = iL x B = qv x B

OK, now think about dropping that differential in there, and replacing B with r-hat. Magically, you get the numerator of the integrand:

idL x r-hat

The only other change is to move mu to the numerator when you replace epsilon, but that is a no-brainer based on comparing Gauss' Law to Ampere's Law, not to mention the fact that it is the epsilon that is in the 'wrong' place because everything about capacitors and electric fields is "upside down" relative to inductors and magnetic fields in AC circuits.