### Finding Quenching Field Magnitude Using Levitation Force: Lab Book 2014_09_29

Summary:  Working more on using the superconductor to detect its own quenching field.  The initial setup is shown below.  The quenching test is described in the following.  A YBCO superconductor is placed between the poles of a very uniform magnet and then cooled into its superconducting state.  The field frozen into the sample at the state transition opposes the fringing fields on the magnet.  However, had the magnetic field been strong enough to quench the superconductor, the results would have been the pendulum swinging freely beyond the pole pieces' diameter until it encountered a field less than its critical field at which point, it would have re-entered the superconducting state and frozen in those field lines, suspending itself.  There's another realization of this process that will be tested today.  The pendulum is again suspended in a uniform field and the field is slowly increased.  It is suspected the sample will be deflected until the quenching field is reached at which point, the pendulum will fall back to its equilibrium vertical position.  By measuring the angle of the pendulum, the levitation field could also be determined.

The superconductor is placed in a Styrofoam cup supported on a wood plank wedged between the two poles of the magnet.   The magnet gap was set at 2 and 9/16 inches.  This could be much smaller for the sample used here, I just need to find a smaller reservoir.

There are two movies.  The first contains the cooler alarm going off.  After the alarm went off, the magnet current supply was slowly ramped down, and water was added to the reservoir after the cooler was switched off.  The cooler alarm did not start again after it was turned back on, nor when the magnet supply was ramped up to 49 amps.

The second movie detailed the superconductor not moving while the reservoir slipped out from underneath it.
We’re measuring the magnetic field with a F. W Bell 5180 Hall Effect Gauss meter.
7.32 – 7.35 kG at a 2 and 9/16 inch gap.

12.8 kG at the gap setting, 1 and 1/8 inch gap setting.
A small Dewar was carved from blue Styrofoam to fit in the smaller gap space, see the first picture below.  The Dewar was suspended as a pendulum between the poles of the magnet as shown in the second picture below.  Dental floss was used to support the Dewar pendulum from the upper yoke of the electromagnet.

The quenching test was as follows:
A YBCO superconductor is placed between the poles of a very uniform magnet and then cooled into its superconducting state.  The field frozen into the sample at the state transition opposes the fringing fields on the magnet.  However, had the magnetic field been strong enough to quench the superconductor, the results would have been the pendulum swinging freely beyond the pole pieces' diameter until it encountered a field less than its critical field at which point, it would have re-entered the superconducting state and frozen in those field lines, suspending itself.  There's another realization of this process that will be tested today.  The pendulum is again suspended in a uniform field and the field is slowly increased.  It is suspected the sample will be deflected until the quenching field is reached at which point, the pendulum will fall back to its equilibrium vertical position.  By measuring the angle of the pendulum, the levitation field could also be determined.

The fringe field produced at the edge of the electromagnet pole, mentioned above, is shown in the diagram below from Lawrence's cyclotron patent application.  Note that the 'magnetic lines of force' become less uniform as the edge of the pole piece is approached.

The small YBCO sample did not quench at this gap and field setting.
Note in the video that at 35 amps during the ramp down, the sample seems to be drawn to the pole piece .  At 10 amps, the lower right corner of the Dewar relaxes.

Anonymous said…
Wow this is interesting video. I understand what your doing but tottally stupid video.
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### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

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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 differe…

### Division: Distributing the Work

Our unschooling math comes in bits and pieces.  The oldest kid here, seven year-old No. 1 loves math problems, so math moves along pretty fast for her.  Here’s how she arrived at the distributive property recently.  Tldr; it came about only because she needed it.
“Give me a math problem!” No. 1 asked Mom-person.

“OK, what’s 18 divided by 2?  But, you’re going to have to do it as you walk.  You and Dad need to head out.”

And so, No. 1 and I found ourselves headed out on our mini-adventure with a new math problem to discuss.

One looked at the ceiling of the library lost in thought as we walked.  She glanced down at her fingers for a moment.  “Is it six?”

“I don’t know, let’s see,” I hedged.  “What’s two times six?  Is it eighteen?”

One looked at me hopefully heading back into her mental math.

I needed to visit the restroom before we left, so I hurried her calculation along.  “What’s two times five?”

I got a grin, and another look indicating she was thinking about that one.

I flashed eac…