# 12.7 Magnetism in matter  (Page 4/13)

 Page 4 / 13

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.

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.

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.

## 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 ${I}_{0}=0.20\phantom{\rule{0.2em}{0ex}}\text{A}?$ (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
$\begin{array}{ccc}\hfill {B}_{0}& =\hfill & {\mu }_{0}n{I}_{0}=\left(4\pi \phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}\text{T}·\text{m/A}\right)\left(2000\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}\text{m}\right)\left(0.20\phantom{\rule{0.2em}{0ex}}\text{A}\right)\hfill \\ \hfill {B}_{0}& =\hfill & 5.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\text{T}.\hfill \end{array}$
2. From inspection of the magnetization curve of [link] , we see that, for this value of ${B}_{0},$ $B=1.4\phantom{\rule{0.2em}{0ex}}\text{T}.$ 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
$\chi =\frac{B}{{B}_{0}}-1=\frac{1.4\phantom{\rule{0.2em}{0ex}}\text{T}}{5.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\text{T}}\text{−1}=2.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}.$

## 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.

#### Questions & Answers

A proton initially at rest falls through a p.d of 25000V. what speed does it gain?
Minister Reply
what is the reaction of heat on magnet
ORIZINO Reply
what is a physical significant of electric dipole moment .
PRANAB Reply
A dipole moment it's a mechanical electrical effect used in nature
Antonio
what is the uses of carbon brushes in generator
Malik Reply
at what temperature is the degree Fahrenheit equal to degree Celsius
Grace Reply
Celsius and Faharaneith are different, never equal
Antonio
find their liners express of n=a+b/T² ( plot graph n against T)
Donsmart Reply
Radio Stations often advertis "instant news,,if that meens you can hear the news the instant the radio announcer speaks it is the claim true? what approximate time interval is required for a message to travel from Cairo to Aswan by radio waves (500km) (Assume the waves Casbe detected at this range )
mahmod Reply
what is growth and decay
Pawan Reply
thevenin
Oladejo Reply
Can someone please predict the trajectory of a point charge in a uniform electric field????
erlinda Reply
what is deference between strong force and coulomb force
zahid Reply
so basically the electric lines or the field lines
zach Reply
it's the measure of the flow of an electric field through a certain area
zach Reply
What is electric flux
Pranju Reply
how to calculate the magnetic force if the B field is depend on the coordinate
Ivan Reply

### Read also:

#### Get the best University physics vol... course in your pocket!

Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

 By Anonymous User By Jordon Humphreys By