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U B = 1.9 × 10 −23 J .

At a room temperature of 27 °C , the thermal energy per atom is

U T k T = ( 1.38 × 10 −23 J/K ) ( 300 K ) = 4.1 × 10 −21 J ,

which is about 220 times greater than U B . Clearly, energy exchanges in thermal collisions can seriously interfere with the alignment of the magnetic dipoles. As a result, only a small fraction of the dipoles is aligned at any instant.

The four sketches of [link] furnish a simple model of this alignment process. In part (a), before the field of the solenoid (not shown) containing the paramagnetic sample is applied, the magnetic dipoles are randomly oriented and there is no net magnetic dipole moment associated with the material. With the introduction of the field, a partial alignment of the dipoles takes place, as depicted in part (b). The component of the net magnetic dipole moment that is perpendicular to the field vanishes. We may then represent the sample by part (c), which shows a collection of magnetic dipoles completely aligned with the field. By treating these dipoles as current loops, we can picture the dipole alignment as equivalent to a current around the surface of the material, as in part (d). This fictitious surface current produces its own magnetic field, which enhances the field of the solenoid.

Figure a shows a rod with randomly oriented magnetic dipoles. Figure b shows domains that got partially oriented after the magnetic field was applied along the axis of the rod. Figure c shows fully oriented domains. Figure d shows that the dipoles are aligned within the individual domains and are equivalent to a current around the surface of the material. This surface current produces its own magnetic field which enhances the field of the solenoid.
The alignment process in a paramagnetic material filling a solenoid (not shown). (a) Without an applied field, the magnetic dipoles are randomly oriented. (b) With a field, partial alignment occurs. (c) An equivalent representation of part (b). (d) The internal currents cancel, leaving an effective surface current that produces a magnetic field similar to that of a finite solenoid.

We can express the total magnetic field B in the material as

B = B 0 + B m ,

where B 0 is the field due to the current I 0 in the solenoid and B m is the field due to the surface current I m around the sample. Now B m is usually proportional to B 0 , a fact we express by

B m = χ B 0 ,

where χ is a dimensionless quantity called the magnetic susceptibility    . Values of χ for some paramagnetic materials are given in [link] . Since the alignment of magnetic dipoles is so weak, χ is very small for paramagnetic materials. By combining [link] and [link] , we obtain:

B = B 0 + χ B 0 = ( 1 + χ ) B 0 .

For a sample within an infinite solenoid, this becomes

B = ( 1 + χ ) μ 0 n I .

This expression tells us that the insertion of a paramagnetic material into a solenoid increases the field by a factor of ( 1 + χ ) . However, since χ is so small, the field isn’t enhanced very much.

The quantity

μ = ( 1 + χ ) μ 0 .

is called the magnetic permeability of a material. In terms of μ , [link] can be written as

B = μ n I

for the filled solenoid.

*Note: Unless otherwise specified, values given are for room temperature.
Magnetic susceptibilities
Paramagnetic Materials χ Diamagnetic Materials χ
Aluminum 2.2 × 10 −5 Bismuth −1.7 × 10 −5
Calcium 1.4 × 10 −5 Carbon (diamond) −2.2 × 10 −5
Chromium 3.1 × 10 −4 Copper −9.7 × 10 −6
Magnesium 1.2 × 10 −5 Lead −1.8 × 10 −5
Oxygen gas (1 atm) 1.8 × 10 −6 Mercury −2.8 × 10 −5
Oxygen liquid (90 K) 3.5 × 10 −3 Hydrogen gas (1 atm) −2.2 × 10 −9
Tungsten 6.8 × 10 −5 Nitrogen gas (1 atm) −6.7 × 10 −9
Air (1 atm) 3.6 × 10 −7 Water −9.1 × 10 −6

Diamagnetic materials

A magnetic field always induces a magnetic dipole in an atom. This induced dipole points opposite to the applied field, so its magnetic field is also directed opposite to the applied field. In paramagnetic and ferromagnetic materials, the induced magnetic dipole is masked by much stronger permanent magnetic dipoles of the atoms. However, in diamagnetic materials, whose atoms have no permanent magnetic dipole moments, the effect of the induced dipole is observable.

Questions & Answers

Newton's second laws is call with
Dyutee Reply
what is mean by thermodynamics
Prasad Reply
it is study about temperature and it's equilibrium
Its the study of heat and its relation with others kind of energy
state caulombs law clearly
constand Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
ezra Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
what is electrostatics
Hero Reply
the study of charge at rest
@Hero; the study of charges at rest is the electrostatics
okay what is electrostatic?
charge at rest
set of character...
Gauss law, electric fields, dipoles,...
A proton initially at rest falls through a p.d of 25000V. what speed does it gain?
Minister Reply
@Minister; use equation v= sq root(2×eV/m)
what is the reaction of heat on magnet
Magnetization decreases with increase in temperature. But in case of diamagnetic substance heat has no role on magnetization.
what is a physical significant of electric dipole moment .
A dipole moment it's a mechanical electrical effect used in nature
what is the uses of carbon brushes in generator
Malik Reply
to minimize heat
at what temperature is the degree Fahrenheit equal to degree Celsius
Grace Reply
Celsius and Faharaneith are different, never equal
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
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
how do you convert temperature in degree Celsius to Fahrenheit
Celsius x 9/5 +32
Practice Key Terms 6

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