Introductory Physics Laboratory, Faculty of Physics and Geosciences, University of Leipzig

Home , Hysteresis, Magnetization, Remanence

E 6e Magnetization Curve and Hysteresis Loop

Tasks

1 Record the initial (virgin) magnetization curve and the (sheared) hysteresis curve B=B(H0) of a ferromagnetic circuit with air gap using a teslameter (Hall-sensor)! Represent graphically the initial magnetization curve and the hysteresis curve in one diagram! Determine the apparent remanence BR* and the coercivity HC graphically!

2 Develop the true (backsheared) hysteresis curve B(HFe) by backshearing the measured hysteresis curve B(H0)! Determine the true remanence BR!

3 Determine the values of the relative permeability µ* of the magnetic circuit using of the initial magnetization curve! Represent graphically the µ* values in dependence on H0! Calculate the permeability µr,max of the core material!

Literature

Physics, P. A. Tipler, 3rd Edition, Vol. 2, Chapt. 27-1, 27-4, 25-4 (toroid) Physikalisches Praktikum, Hrsg. D. Geschke, B. G. Teubner Verlag Stuttgart-Leipzig, 12th Edition, (in German), Electricity, Chapt. 2.0.3, 2.3 Ferromagnetism http://en.wikipedia.org/wiki/Ferromagnetism

Accessories

DC laboratory power supply, teslameter, multimeter, toroid with iron core (core with air-gap), variable-ratio transformer to demagnetize the test material (by the demonstrator)

Keywords for preparation

- relation between magnetic circuit voltage, magnetic field and magnetic flux density of a toroidal iron filled coil with and without air-gap - magnetization, permeability, susceptibility - diamagnetism, paramagnetism, ferromagnetism, Curie temperature - hysteresis curve, remanence, coercivity - principle of teslameter (Hall effect)

Remarks

Before beginning the experiment the toroidal material has to be demagnetized by the demonstrator.

In task 1 you have to measure the initial magnetization curve (virgin curve) between the points 0 and P1 in Fig.1 and the (sheared) hysteresis curve between the points P1→P2, (after reversing the direction of the current) → P3 stepwise by changing of the coil current I at given values (H0 ∼ I ).

You should create a plot B versus H0 and a new plot for the backsheared curve (B versus HFe ) between the points P1 and P2 to determine the remanent field BR as shown in Fig.1.

1 Fig. 1

Backshearing of the hysteresis curve

The following relations between the magnetic induction B and magnetic field HFe in iron, HLu in air and H0 in the magnetic circuit are valid: I B = µ µ H = µ H = µ µ *H , H = N N - number of turns of toroidal coil (toroid) 0 r Fe 0 Lu 0 0 0 l From Ampere´s law follows H Fe lFe + H Lu d = H 0 l with lFe length of iron core, l = lFe + d, d width of air gap, and with the condition d<

B d H Fe = H 0 − . (Derive it!) µ0 l

The magnetic field HFe is reduced by [B d/(µ0 l)]. The curve B = B(H0) is called as sheared hysteresis curve.

The permeability µ* of the magnetic circuit is not the permeability µ r of iron. One can get the nonsheared or true hysteresis curve B = B(HFe) by backshearing of the sheared hysteresis curve. At the graphic method the wanted correction value for a certain value B1 can be determined using a straight line through the points

(0,0) and [ (B1/µ 0 )( d/l ), B1 ] as shown in Fig. 2.

−1 ⎛ 1 d ⎞ The value µ of the iron core can be calculated from the µ * value using the equation µ = ⎜ − ⎟ . r,max max r ⎜ * ⎟ ⎝ µ l ⎠ (Derive this equation!)

An estimation of uncertainty has to be carried out for µr,max , for true remanence Brw and for coercivity Hc.

2 Fig. 2 To the graphic procedure of backshearing

Hints to experiment E 6e

Data to the Toroids

Toroid I Toroid II Toroid III

average length l (390±5) mm (390±5) mm (290±5) mm

gap width d (2,0±0,2) mm (2,0±0,2) mm (2,0±0,2) mm

cross-section area A 900 mm2 900 mm2 750 mm2

number of turns N 2000 2000 2000

Measure the initial magnetization curve from points 0 to P1 (Fig. 1) at the following currents I : I= 0,05; 0,1; 0,2; 0,3; 0,4; 0,5; 0,6; 0,8; 1,0; 1,5; 2,0; 2,5; 3,0; 3,5 A.

To measure the hysteresis curve in the first quadrant (from P1 to P2) you have to decrease the current in the same steps (I = 3,0; 2,5;...;0 A). Then you have to reverse the polarity of the voltage to measure the

hysteresis curve from P2 to P3. The value HC shall be determined with highest accuracy!

Hysteresis

When a ferromagnetic material is magnetized in one direction, it will not relax back to zero magnetization when the imposed magnetizing field is removed. It must be driven back to zero by a field in the opposite direction. If an alternating magnetic field is applied to the material, its magnetization will trace out a loop called a hysteresis loop. The lack of retraceability of the magnetization curve is the property called hysteresis and it is related to the existence of magnetic domains in the material. Once the magnetic domains are reoriented, it takes some energy to turn them back again. This property of ferromagnetic materials is useful as a magnetic "memory". Some compositions of ferromagnetic materials will retain an imposed magnetization indefinitely and are useful as "permanent magnets". The magnetic memory aspects of iron and chromium oxides make them useful in audio tape recording and for the magnetic storage of data on computer disks.

from hyperphysics http://hyperphysics.phy-astr.gsu.edu/hbase/solids/ferro.html

Hysteresis in Magnetic Recording

Because of hysteresis, an input signal at the level indicated by the dashed line could give a magnetization anywhere between C and D, depending upon the immediate previous history of the tape (i.e., the signal which preceded it). This clearly unacceptable situation is remedied by the bias signal which cycles the oxide grains around their hysteresis loops so quickly that the magnetization averages to zero when no signal is applied. The result of the bias signal is like a magnetic eddy which settles down to zero if there is no signal superimposed upon it. If there is a signal, it offsets the bias signal so that it leaves a remnant magnetization proportional to the signal offset.