MODERN PHYSICS (PHY 320) LAB

## Magnetic Materials and Electromagnets

OBJECT:

To investigate some magnetic properties of matter.
To determine some properties of the magnetic fields of various permanent magnets.
To measure the  magnetic field variations of an electromagnet as a function of the coil current.
To investigate the Ising model of magnetism.
To investigate thermal demagnetization.

APPARATUS:

A set of six Neodymium-Iron-Boron disk magnets with several 1 mm plastic spacers.
A set of six Ceramic permanent magnets with several 1 mm plastic spacers.
A large Cenco electromagnet with variable gap and coils to handle currents up to 15 A, associated power supply and current regulator.
F.W.Bell Gauss/Tesla Meter model 4048 for precision magnetic field measurements.
Pasco Gauss Meter and Science Workshop interface.

BACKGROUND:

In the study of magnetism and the magnetic effects associated with the motion of electric charges, one usually designates symbols B, H, M, and µ to describe magnetic properties.

B =  the quantity known as the magnetic induction, or the magnetic flux density.  It is this property of magnetic fields that determines the force that is exerted upon a current or a moving charge.

H =  the term referred to as magnetic intensity, or field strength.  More descriptively,  it is a field caused by conduction currents.  In a region where there is no magnetic material, B = µo H.

M =  the term named the magnetic polarization or magnetization and defined as the magnetic moment per unit volume within any magnetic material.  In a region where there are no fields due to conduction currents, B = µo M.

All of the above are vector quantities.

µ = a magnetic property of matter called the permeability.  In isotropic media, it is a scalar quantity, and in many materials, like free space or non-magnetic materials, it is a constant µo.

For most materials, the relationship between these fields can be expressed in either of two ways:

B = µo ( H + M)     or       B = µ H

Reference is frequently made to the example of a solenoid with some material used as the core of the windings to relate these terms.  Recall that inside the solenoid with n turns per unit length and a current I in the coil, we have approximately

B = µnI    and        H = B/µ = nI     (independent of the core material).

Thus, a current in the coil produces the magnetic intensity H throughout the core, and this sets up a flux density B which consists of a contribution from both the coil's field H and the material's magnetization M.

The most easily observed of all magnetic effects is ferromagnetism, so called because of its occurrence in metallic iron and a number of iron compounds.  The experimental facts about ferromagnetic materials include that

• In these materials, very large magnetizations can be obtained.
• In these materials, M is not usually proportional to H as it is in most other materials. i.e., the value of M depends not only on the value of the applied field but also on the previous history of the sample.
• In some cases, a sample may retain its magnetization even in the absence of of an external applied field.
• These very same materials that show such large permanent magnetization can also exist in a state with little or no net magnetization.
• In these materials, there is a strong tendency for the material to break up into many magnetic domains (regions where all dipoles are aligned), each with a different direction of magnetization, so that the macroscopic effect is to give zero magnetization.

The behavior of a magnetic material during magnetization is conventionally presented as a B-H plot.

·         The origin of coordinates 0, represents the unmagnetized condition of a ferromagnetic sample.  When a magnetizing force is applied, the sample proceeds along the black line to point a as the magnetic polarization increases.  This line is known as the magnetization curve.

·         When the magnetizing force at point (a) is reduced, the flux density does not reduce back along the magnetization curve, but displays higher values.  When H has been reduced to zero, B still has a positive value indicated by point (b) which is known as the remanence, a measure of its retentivity. This phenomenon is known as hysteresis.

·         In order to bring B back to zero, the magnetizing force must be made negative, to a value indicated by point (c) where H has a value known as the coercive force, a measure of its coercivity.

·         When H is varied periodically about the origin the closed contour is known as a hysteresis loop.

·         The portion of the loop which lies in the second quadrant is known as the demagnetization curve.   This is the portion of interest in a discussion of permanent magnets.   In  general, it is desirable that permanent magnets have a large remanence to retain a great portion of the magnetization, and  a large coercive force in order that the magnet will not easily be demagnetized. The best single figure of merit of a permanent magnet is the maximum value of the product BH along the demagnetization curve.  Since the product BH has the dimensions of energy density, it is referred to as the energy  product and the maximum value as the maximum energy product  BHmax.

Dexter Magnetic Technologies supplies a great deal of helpful magnet background material online in their Design and Reference Manual !!! Check it out!!!

### Experiment 1:    NdFeB permanent magnets

Precautions:

• These magnets should never be brought close to cassette tapes, floppy disks, bank cards, telephone cards or any other magnetic card.
• Handle carefully to prevent having a finger caught between two magnets.  This force may be great enough to cause a blood blister or an abrasion.
• When bringing two magnets together, be sure to do it slowly. Otherwise the magnets will forcibly strike each other, and chipping  of the surface may result.
• If it is difficult to separate magnets, press one against the edge of a desk and slide the other one free.

A.   Flux density versus gap length

1. Use the slotted plastic spacer to separate two magnet disks. Insert the tip of the Gauss/Tesla meter probe 1900 into the slot. Slide the probe tip along the length of the slot to find the maximum field reading.  Record it.
2. Add two spacers on either side of the slotted spacer to separate the disks and repeat the procedure.
3. Continue to add spacers two at a time and record the corresponding measurements for each different gap up to as many spacers as you have.
4. Plot Bg versus Lg.  At the Dexter Magnetic Technologies website, find the appropriate relation and fit your data to it.

B.    Flux density versus magnet volume (length)

1. Use the slotted plastic spacer to separate two magnet disks. Insert the tip of the Gauss/Tesla meter probe 1900 into the slot. Slide the probe tip along the length of the slot to find the maximum field reading.  Record it.
2. Add a third magnet disk on one side of the pair and repeat the procedure.
3. Continue to add magnet disks one at a time and record the corresponding measurements for each different magnet length.  It may also be helpful to record the field just outside the face of a single magnet disk.
4. Plot Bg versus Lm (total length of magnets).  At the Dexter Magnetic Technologies website, find the appropriate relation and fit your data to it.

### Experiment 2:    Ceramic permanent magnets

A.   Flux density versus gap length

1. Use the slotted plastic spacer to separate two magnet disks. Insert the tip of the Gauss/Tesla meter probe 1900 into the slot. Slide the probe tip along the length of the slot to find the maximum field reading.  Record it.
2. Add two spacers on either side of the slotted spacer to separate the disks and repeat the procedure.
3. Continue to add spacers two at a time and record the corresponding measurements for each different gap up to as many spacers as you have.
4. Plot Bg versus Lg.   Compare to Experiment 1A.

B.    Flux density versus magnet volume (length)

1. Use the slotted plastic spacer to separate two magnet disks. Insert the tip of the Gauss/Tesla meter probe 1900 into the slot. Slide the probe tip along the length of the slot to find the maximum field reading.  Record it.
2. Add a third magnet disk on one side of the pair and repeat the procedure.
3. Continue to add magnet disks one at a time and record the corresponding measurements for each different magnet length.  It may also be helpful to record the field just outside the face of a single magnet disk.
4. Plot Bg versus Lm (total length of magnets).  Compare to Experiment 1B.

### Experiment 3:     Electromagnet

Flux density versus current:  Hysteresis

1. Zero the Pasco Gauss Meter probe in the transverse (radial) configuration away from the electromagnet.
2. Place the tip of the Gauss Meter in the center of the field of the electromagnet and record the magnitude and sign of the residual field.
3. Move the electrical connection on the Current Control box to Reverse, then measure the current necessary to zero the magnetic field, a measure of the coercivity.
4. Increase the coil current in 0.5A steps and record the meter reading until the maximum current is reached.  You must simultaneously use both current controls and keep the control indicator between 2 and 6.
5. Reduce the coil current in 0.5A steps and record the meter reading.  Measure the new residual field.
6. Turn off the power supplies and move the electrical connection on the Current Control box to Normal.
7. Repeat steps 3, 4 and 5.
8. Plot Bg versus  I, the hysteresis curve for this magnet.  Identify the retentivity and coercivity, (you will need to zoom in at values near the origin).

### Experiment 4:    Ising Model of ferromagnetism

Go to the Ising model physlet found at http://webphysics.davidson.edu/Applets/ising/default.html.  Then go to the Time Development page and plot the magnetization as a function of time.

1.      Starting at T=0, find the maximum temperature at which all of the spins are aligned.  Keep B=0.

2.      Measure the hysteresis width, twice the coercivity, for T=0, 1, 2, 3, and 4.

3.      Measure and plot M vs. B for T = 0, T < Tc, and T > Tc.

4.      Using the energy plot, determine the "internal energy" or "self energy" at T=0, B=0.  What is the total energy difference between the T=0 and T = ∞ cases? (You can type in temperatures greater than the maximum value of the slider.)  What is the difference in energy between the parallel and anti-parallel spin states?  The interaction energy is given by E=Js*s. Determine J, the strength of the interaction between spins.

5.      Find the energy splitting and shift for the parallel and anti-parallel spin states for B=5.

### Experiment 5:    Temperature Dependence of Demagnetization

Precautions:

• When handling the 4 kG Neodymium-Iron-Boron (NdFeB) permanent magnets or using the 11 kG electromagnet, be careful to keep floppy disks, bank cards, telephone cards, electronic watches, calculators, digital cameras, etc. away from the magnets.  The high field strengths may cause permanent damage to such items.

• Exercise extreme care when working around the hot plate or handling hot materials.  Temperatures in excess of 400 deg. Celsius will be reached in this experiment which can result in severe burns.

A.  Demagnetization versus Temperature

1.      Zero the Gauss/Tesla meter probe 1900.  Find and record the maximum field reading by slowly sliding the probe tip over the NdFeB magnet.

2.      Insert the NdFeB magnet into the magnet recess of the magnet/temperature probe holder.  Check the field to see that the “negative” pole faces up when in the holder. Place the holder assembly directly on the center of the hot plate and positioned under the glass cup containing the magnetic field sensor.  The holder should lay perfectly flat on the hot plate, and a small clearance gap must exist between the hot plate and the temperature probe shaft.

3.      Set up your data acquisition sensors in Data Studio to graph Temp. vs Time, Magnetic Field vs Time, and Magnetic Field vs Temp.  Be sure to select the “type K” thermocouple temperature sensor.  The magnetic field sensor properties should be set to the x10, gauss, and medium sensitivity scales.  (Tip: plan ahead by setting the graph ranges to 350 C., 50 gauss and 1300 seconds).

4.      Slightly tilt the clamp-pole-glass cup assembly away from the hot plate, and move the entire assembly slightly away from the hot plate.  Switch the magnetic field probe to the axial mode and zero the probe.  Run Data Studio for a few seconds to be sure that the probe reads zero.  Replace the clamp-pole-glass cup assembly back over the hot plate and magnet holder.  The probe in the glass cup should be centered just above the lowest point of curvature in the cup and directly over the magnet.  The glass cup should be as close as possible to the magnet holder, but should not touch any part of it.  Turn on the air supply to about the “2-o’clock” position.  It is critical that air flows around the probe tip to cool the sensor and prevent the Hall signal from drifting erroneously.

5.      Prepare the electromagnet to receive the hot magnet by slowly turning on the cooling water to a gentle flow.  Then bring the electromagnet up to full current gradually, while maintaining the current regulator’s indicator in mid-range.

6.      Clear your Data Studio screens and prepare a checklist of elapsed time (seconds) for each hotplate setting.  When ready, trigger the run mode.  After about 10 seconds, very carefully adjust the hot plate setting to position 2 (the first “on” position).  Be very careful not to jiggle the hot plate when adjusting the settings, or bump the table while taking data (this may cause your magnetic field sensor to move)!   Increase the temperature setting to the next position (3, 4, 5, … ,10) every 150 seconds precisely.  After the last temperature setting, continue to take data until approximately 1300 seconds, and then stop the run and save your data.

7.      Examine your data.  Are the curves smooth?  Based on your data, what is the Curie temperature for your magnet? What would be the maximum operating temperature for your magnet, if you don’t want to seriously degrade the magnet’s strength? Go to the following website:  ( http://www.tdk.co.jp/tefe02/magnet.htm ).  Look at the curves on page 47 and 50. Which material series curve comes closest to matching your curve? (Hint: look at the temperature for the “knee” where the field begins to sharply drop off and compare to your data).

B.  Re-magnetization of the NdFeB Permanent Magnet

1.        With the hot plate still on and the temperature reading still around 350 degrees Celsius, carefully remove the hot magnet/temperature probe holder.  Quickly “dump” the magnet into the long handled magnet carrier, close and tighten the cover, and place the magnet between the pole pieces of the electromagnet.  There is a notch on the side of the magnet carrier which indicates the location of the magnet.  Be sure to keep this mark centered between the pole pieces where the field is uniform.

2.        Keep the magnet carrier in the field for five minutes while it cools.  Then slowly turn down the electromagnet current to zero, remove the magnet carrier from between the poles, remove the magnet from the carrier, and measure its’ field with the Gauss/Tesla meter probe 1900.

3.        How does the restored field compare with your original field measurement before heating?  Calculate the percent difference. If it is now significantly lower, then you were probably too slow in getting the magnet into the magnet carrier and then over into the re-magnetizing field.  This must be done quickly before the magnet has time to cool down and “freeze-in” the domain arrangements.  If the field is appreciably lower than the initial field, then re-heat the magnet to around 350 degrees Celsius holding it at that temperature until thermal equilibrium is reached, then repeat the re-magnetization procedure.