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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?


(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] .


  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 .


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

if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
what is electrostatics
Yakub Reply
Study of charges which are at rest
Explain Kinematics
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Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
LOAK Reply
he's the father of 3 newton law
he is Chris Issaac's father :)
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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