### Update on the NMSU Superconductor Gravity Experiment

First, a recap:

In 1992 Eugene Podkletnov reported a possible gravitational field shielding from a rotating, levitated superconductor. NASA tried to duplicate his experiment but didn't complete it. We were able to borrow NASA'S equipment to attempt to replicate Podkletnov's experiment. After quite a bit of research it became clear that none of the replication attempts have succeeded in levitating the semiconductor, (via the Meissner effect and flux pinning), at the magnetic field frequencies specified by Podkletnov. At this point we backed up and decided to study the dependence of the levitation force with respect to frequency. All this is detailed more fully in the presentation below.

I've been working on a torsion balance to measure the levitation force. The balance isn't my design, I found it in the Review of Scientific Instruments.
 From NMSUSCGE

The balance consists of a stretched steel wire with an attached boom that is free to rotate. When a steel wire is twisted, it behaves like a spring. The force exerted by the wire is proportional to the angle the wire has been twisted through. By measuring the angle, we can measure the force exerted by the electromagnet, (on the tabel), on the superconductor in the sample holder at the end of the boom. So, in the following video, the higher the boom of the balance swings up, the greater the levitation force on the superconductor.

I've been through three different sample holder designs so far. The first utilized a rubber key cover to hold the superconductor. This design mostly didn't work because in the amount of time it took to insert the superconductor, it warmed up to much and reverted back to its normal, non-superconducting state. The second and third designs utilized IC chip holders inverted and suspended from the end of the bin. With this design, the superconductor is immersed in liquid nitrogen, (see below), until the electromagnet is turned on.

Picture of the day
 From Jun 21, 2012

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

### Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…