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This picture shows a plot of the total field in the material versus the applied field for an initially unmagnetized piece of iron. The initial increase in the total field is followed by the saturation.
(a) The magnetic field B in annealed iron as a function of the applied field B 0 .

When B 0 is varied over a range of positive and negative values, B is found to behave as shown in [link] . Note that the same B 0 (corresponding to the same current in the solenoid) can produce different values of B in the material. The magnetic field B produced in a ferromagnetic material by an applied field B 0 depends on the magnetic history of the material. This effect is called hysteresis    , and the curve of [link] is called a hysteresis loop. Notice that B does not disappear when B 0 = 0 (i.e., when the current in the solenoid is turned off). The iron stays magnetized, which means that it has become a permanent magnet.

This picture shows a typical hysteresis loop for a ferromagnet. It starts at the origin with the upward curve that is the initial magnetization curve to the saturation point a, followed by the downward curve to point b after the saturation, along with the lower return curve back to the point a.
A typical hysteresis loop for a ferromagnet. When the material is first magnetized, it follows a curve from 0 to a . When B 0 is reversed, it takes the path shown from a to b . If B 0 is reversed again, the material follows the curve from b to a .

Like the paramagnetic sample of [link] , the partial alignment of the domains in a ferromagnet is equivalent to a current flowing around the surface. A bar magnet can therefore be pictured as a tightly wound solenoid with a large current circulating through its coils (the surface current). You can see in [link] that this model fits quite well. The fields of the bar magnet and the finite solenoid are strikingly similar. The figure also shows how the poles of the bar magnet are identified. To form closed loops, the field lines outside the magnet leave the north (N) pole and enter the south (S) pole, whereas inside the magnet, they leave S and enter N.

The left picture shows magnetic fields of a finite solenoid; the right picture shows magnetic fields of a bar magnet. The fields are strikingly similar and form closed loops in both situations.
Comparison of the magnetic fields of a finite solenoid and a bar magnet.

Ferromagnetic materials are found in computer hard disk drives and permanent data storage devices ( [link] ). A material used in your hard disk drives is called a spin valve, which has alternating layers of ferromagnetic (aligning with the external magnetic field) and antiferromagnetic (each atom is aligned opposite to the next) metals. It was observed that a significant change in resistance was discovered based on whether an applied magnetic field was on the spin valve or not. This large change in resistance creates a quick and consistent way for recording or reading information by an applied current.

Photo shows the inside of a hard disk drive. The silver disk contains the information, whereas the thin stylus on top of the disk reads and writes information to the disk.
The inside of a hard disk drive. The silver disk contains the information, whereas the thin stylus on top of the disk reads and writes information to the disk.

Iron core in a coil

A long coil is tightly wound around an iron cylinder whose magnetization curve is shown in [link] . (a) If n = 20 turns per centimeter, what is the applied field B 0 when I 0 = 0.20 A ? (b) What is the net magnetic field for this same current? (c) What is the magnetic susceptibility in this case?

Strategy

(a) The magnetic field of a solenoid is calculated using [link] . (b) The graph is read to determine the net magnetic field for this same current. (c) The magnetic susceptibility is calculated using [link] .

Solution

  1. The applied field B 0 of the coil is
    B 0 = μ 0 n I 0 = ( 4 π × 10 −7 T · m/A ) ( 2000 / m ) ( 0.20 A ) B 0 = 5.0 × 10 −4 T .
  2. From inspection of the magnetization curve of [link] , we see that, for this value of B 0 , B = 1.4 T . Notice that the internal field of the aligned atoms is much larger than the externally applied field.
  3. The magnetic susceptibility is calculated to be
    χ = B B 0 1 = 1.4 T 5.0 × 10 −4 T −1 = 2.8 × 10 3 .

Significance

Ferromagnetic materials have susceptibilities in the range of 10 3 which compares well to our results here. Paramagnetic materials have fractional susceptibilities, so their applied field of the coil is much greater than the magnetic field generated by the material.

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Questions & Answers

in the 2nd example, for chapter 8.2 on page 3/3, I don't understand where the value 48uC comes from, I just couldn't get that value in my calculator.
Anita Reply
what is electromagnetic force. do electric and magnetic force happen differently
Short Reply
yes
Renugadevi
yes
Pranay
why
Godson
how?
Godson
derived the electric potential due to disk of charge
aron Reply
how can we derived potential electric due to the disk
aron
how can you derived electric potential of a disk
aron
how can you derived electric potential due to disk
aron
where is response?
aron
what is difference between heat and temperature?
Qasim Reply
temperature is the measure of degree of hotness or coldness. on the other hand, heat is the form of energy, which causes temperature. So we can safely say, heat is the reason and temperature is its consequence.
SABYASACHI
how many liquid metals do we have
Jeffery Reply
do we have gasses as metals
Jeffery
who knows should please tell us
Sadiku
yes...gallium & cesium
Idris
Hg is liquid. No metal gasses at standard temp and pressure
Shane
I don't ever understand any of this formulae
isaac Reply
which formula
Sadiku
How to determine a temperature scale
Masia Reply
what is the formula for absolute error
Nyro
define kelvin planck statement
Masia Reply
using p-v diagram, explain what takes place during each four processes of a carnot cycle
Masia
using p-v diagram, explain what takes place during each four processes of a carnot cycle
Masia
state zeroths law of thermodynamics
Masia Reply
The zeroth law of thermodynamics states that if twothermodynamic systems are each in thermal equilibrium with a third one, then they are in thermal equilibrium with each other
Seza
zeroth law of thermodynamic state that when a body A and B are in thermal equilibrium to body C ,a state is attained when body A,B and C are in thermal equilibrium.
akanbi
sorry guys I got no any idea on the law can someone help me please?
SNAHR
hi
Muhsin
The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third one, then they are in thermal equilibrium with each other. Accordingly, thermal equilibrium between systems is a transitive relation. Two systems are said to be in the relation of
Muhsin
I can help u Snahr as possible
Vinayaka
it simply states that, if two bodies are separately in thermal equilibrium with a third body, then those two bodies will also be in thermal equilibrium with each other
Vinayaka
What mass of steam of 100 degree celcius must be mixed with 150g of ice at 0 degree celcius, in a thermally insulated container, to produce liquid water at 50 degree celcius
Emmanuel Reply
sorry I dont know
Bamidele
thank you
Emmanuel
What is the pressure?
SHREESH
To convert 0°C ice to 0°c water. Q=M*s=150g*334J/g=50100 J.......... Now 0° water to 50° water... Q=M*s*dt=150g*4.186J/g*50= 31395 J....... Which adds upto 81495 J..... This is amount of heat the steam has to carry. 81495= M *s=M*2230J/g..therefore.....M=36.54g of steam
SHREESH
This is at 1 atm
SHREESH
If there is change in pressure u can refer to the steam table ....
SHREESH
instrument for measuring highest temperature of a body is?
brian Reply
Thermometer
Umar
how does beryllium decay occur
Sandy Reply
Photon?
Umar
state the first law of thermodynamics
Kansiime Reply
Its state that "energy can neither be created nor destroyed but can be transformed from one form to another. "
Ayodamola
what about the other laws can anyone here help with it please
Sandy
The second law of thermodynamics states that the entropy of any isolated system always increases. The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.
sahil
The first law is very simple to understand by its equation. The law states that "total energy in thermodynamic sytem is always constant" i.e d¶=du+dw where d¶=total heat du=internal energy dw=workdone... PLEASE REFER TO THE BOOKS FOR MORE UNDERSTANDING OF THE CONCEPT.
Elia
what is distance.?
Ali Reply
what is physics?
Ali
Physics is a scientific phenomenon that deals with matter and its properties
Ayodamola
physics is the study of nature and science
John
Chater1to7
min
Physics is branch of science which deals with the study of matters in relation with energy.
Elia
What is differential form of Gauss's law?
Rohit Reply
Practice Key Terms 6

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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