Domains are well modeled by the compass table, an array of about one hundred small compass needles used for showing fields of bar magnets, etc. When there is no strong external B-field, sections of the array line up in different directions, each individual compass needle aligning itself with the local field. When the array is tapped sharply, it will be seen that the needles on the boundaries of the domains are the least stable (vibrate the most), and some of them realign causing one domain to grow at the expense of another.
In the Barkhausen effect, a large coil of fine wire is connected through an amplifier to a speaker. When an iron rod is placed within the coil and stroked with a magnet, an audible roaring sound will be produced from the sudden realignments of the magnetic domains within the rod. A copper rod, on the other hand, produces no effect.
This pretty demo uses a "permalloy" rod, a soft iron rod, a hammer, and the compass dip needle (which is shown here [1]).
Using the dip needle find the direction of the earth's magnetic field in the class room (plunging about 60° earthward to the magnetic north). Arrange the soft iron rod perpendicular to the earth's field, and strike its end several times with a hammer. This insures that it is demagnetized, which is demonstrated by showing that either end of the rod will attract either end of the compass needle (by magnetic polarization). Now align the rod with the earth's field and strike it several times to shake its domains around and magnetize it. That the rod is magnetized is demonstrated by showing that the north end of the rod repels the north end of the compass needle and the south end of the rod repels the south end of the compass needle. This rod retains its magnetization, no matter how it is oriented in the earth's field.
However, the permalloy rod is so compliant that if held along the earth's field its north end will repel the north end of the compass needle, and now if it is smoothly reversed without any hammer strikes, the other end will repel the north end of the compass needle! Its domains line up with the earth's field without any impact blows.
A small wheel has monel metal wrapped around its circumference. A small light bulb is positioned to heat one part of the circumference, raising the metal above its Curie temperature so it no longer responds to magnetism. When the wheel is placed in the field of a strong magnet, it rotates slowly as one part of the circumference is continually rendered non-magnetic by the heat of the light bulb.
A nickel paper clip (a regular steel one is available too) attached to a base with a string is suspended in air by the use of a magnet. If the nickel paper clip is heated with a lighter (for the steel paper clip a blowtorch is required) beyond a certain temperature called the Curie temperatures it is no longer attracted by the magnet.
The Curie temperature (Tc) is the critical temperature beyond which a previously ferromagnetic material becomes paramagnetic. On the atomic level, below the Curie temperature the magnetic moments, contributed mainly by the electrons, are aligned in their respective domains and even a weak external field results in a net magnetization. As the temperature increases to Tc and above however, fluctuations due to the increase in thermal energy destroy that alignment. Tc for nickel is 631K, while that for iron is 1043K.
A magnetic declination and inclination needle is provided for determining the direction (deviation and dip angle) of the earth's magnetic field in the classroom.
A globe of the earth may help to illustrate these concepts.
The total magnitude of the magnetic field vector is about 0.5 Gauss units or equivalently 50,000 nanoTeslas (nT). To find the components of the magnetic field anywhere visit the Standard magnetic Field Model [2] and enter the date, and your geographic latitude, longitude and elevation. The table below shows the representative components for June 1, 1999 at sea level. Bx, By and Bz are the components in units of nT, B is the total field strength also in units of nT, D is the declination angle between geographic and magnetic north, and I is the inclination or Dip Angle, in degrees below the local horizontal plane.
Average Magnetic Components
City | Bx | By | Bz | B | D | I |
Los Angeles | 24276 | 5996 | 41636 | 48568 | 13.9 | 59.0 |
New York | 19308 | -4643 | 50289 | 54068 | -13.5 | 68.5 |
Boston | 18006 | -1566 | 53490 | 56461 | -4.9 | 71.3 |
Chicago | 18686 | -803 | 52908 | 56117 | -2.5 | 70.5 |
Miami | 25478 | -2182 | 38586 | 46290 | -4.9 | |
Huston | 24892 | 2050 | 42441 | 49245 | 4.7 | 59.5 |
Denver | 20895 | 3878 | 49938 | 54272 | 10.5 | 66.9 |
San Francisco | 23004 | 6411 | 43851 | 49932 | 15.5 | 61.4 |
There are 3 ball bearings stuck to a magnet in a track. A fourth ball bearing is released on the opposite side of the magnet, and is attracted to it. The ball at the other end shoots off at a much higher velocity. Where does the energy come from?
A second version of the gauss cannon is below and uses one spherical magnet which looks identical to the ball bearings. The device can first be shown without the magnet, when it acts like Newton's cradle and conserves energy. With the magnet, the end ball shoots off the end of the ramp.
The circuit below, from Physics Demonstration Experiments Volume 2 by Harry Meiners, page 972, will draw a hysteresis curve on the oscilloscope. The twenty ohm resistor serves to measure the current to the transformer primary producing a horizontal signal proportional to H. The output of the secondary of the transformer is proportional to dB/dt. The final RC circuit integrates this (see RC Integration and Differentiation [3]) to produce a vertical signal proportional to B. As you adjust the variac to control the current to the primary, the curve on the oscilloscope stretches out to saturation.
A compass table with a hundred or so tiny compass needles displays the magnetic field of a bar magnet, or two attracting or repeling magnets, for overhead projection. The compass table replaces the old iron filing magnetic field demonstrations (which are still available).
Compass tables are also used to show the magnetic fields of a long straight wire, a solenoid coil, and a current loop (see Solenoid and Loop Fields [4] and Parallel Wires [5]). The "magniprobe" is a tiny bar magnet completely free to rotate on gimbals in any direction. It will display the three dimensional form of the magnetic field of a bar magnet, delighting the instructor. However, the device is too small to be seen by more than a few students at once unless enlarged on TV. The "Mark II" version of the magniprobe is sensitive enough to detect the earth's field.
A torsional balance contains various vials of paramagnetic and diamagnetic material including graphite and gadoliminium oxide.
Diamagnetic graphite can be used to stabilize magnetic levitation.
Microscopic graphite dust is made of flakes which lie flat and reflect a silver light (left view). When put over a magnetic field, the flakes stand up on edge due to graphite's diamagnetic property (right view). Only the top edges reflect light, and the powder looks very black. Light goes in, scatters into the deep valleys, and never comes out. The blackest black has been produced using a forest of aligned carbon nanotubes.
Rowland's Ring is used to demonstrate the magnetization curve of iron. (See Halliday and Resnick, Part II, Sec. 37.6) We have an actual Ring, or the Leybold demountable transformer will serve.
The flux in the iron is measured by switching off the current in the energizing coil and recording the reading of a ballistic galvanometer hooked to a pickup coil. (You can show that the maximum reading of a ballistic gavanometer is proportional to q = i t, which is in turn proportional to the change in flux through the pickup coil. You can determine the constant of proportionality by discharging a known capacitor through the galvanometers.) The large demonstration galvanometer will serve as a ballistic galvanometer for lecture purposes.
Professor J. Oostens has suggested the following demonstration of magnetic saturation and reluctance:
The Leybold transformer is arranged as above. The experiment is run first with no gap for several values of the current. Then a small gap is provided with shims, and the measurements repeated for the same set of currents. A Hall probe and Gaussmeter can be introduced in the second case for more accurate measurements of B in the gap. Sample data are shown below:
I
(amps) |
nI
(amp.turns) |
GFe
(units) |
GGap
(units) |
BCap
(Tesla) |
<--higher degree of accuracy. |
10 | 2500 | 1.2 | 1.3 | 0.89 |
Some deviation is due to a remiant field. (Iron behaves like a magnet for very low currents) |
5 | 1250 | 1.1 | 0.75 | 0.50 | |
3 | 750 | 0.95 | 0.45 | 0.28 | |
2 | 500 | 0.8 | 0.27 | 0.19 | |
1 | 250 | 0.7 | 0.1 | 0.090 | |
0.5 | 125 | 0.45 | 0.05 | 0.012 |
The graph shows that the field in the iron quickly reaches saturation. By computing the reluctance,
Reluctance = magnetomotive force / flux = nI / Φ
you can show that the reluctance of the air gap is much greater than that of the iron, even though the path length is much smaller.
An undamped compass needle vibrates about equilibrium in a B-field; the vibration frequency can be used as a measure of B. Let the (unknown) moment of inertia of the compass needle be I, and its (unknown) magnetic moment μ. Then the restoring torque τ=Bμsinθ. Using the analogy to linear harmonic motion the angular frequency of vibration is
ω = √ (k/m) = √ (Bμ/I)
Thus, the frequency of vibration of the needle is proportional to √B. Measure the frequency of vibration of the compass needle in the Earth's field of 0.5 gauss, and obtain the strength of other B-fields from these results.
Gauss Meter
Accurate and detailed measurements of B-field can be made with a Gaussmeter and Hall probe. You can illustrate the size of the gauss unit and the strength of various magnets, or make measurements of B-fields for electron deflection, etc.
Links:
[1] https://demoweb.physics.ucla.edu/node/249
[2] http://www.ngdc.noaa.gov/seg/geomag/magfield.shtml
[3] https://demoweb.physics.ucla.edu/node/174
[4] https://demoweb.physics.ucla.edu/node/238
[5] https://demoweb.physics.ucla.edu/node/239