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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

two point charges +30c and +10c are separated by a distance of 80cm,compute the electric intensity and force on a +5×10^-6c charge place midway between the charges
Tijani Reply
what is the difference between temperature and heat
Ishom Reply
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Abdul
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
Gamma
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
TONEJIT Reply
A charge insulator can be discharged by passing it just above a flame. Explain.
Mudassar Reply
of the three vectors in the equation F=qv×b which pairs are always at right angles?
DRASHTI Reply
what is an ideal gas?
Justine Reply
What is meant by zero Kelvin ?
Justine
Why does water cool when put in the pot ?
Justine
when we pour the water in a vessel(pot) the hot body(water) loses its heat to the surrounding in order to maintain thermal equilibrium.Thus,water cools.
rupendra
when we drop water in the pot, the pot body loses heat to surrounded in order to maintain thermal equilibrium thus,water cool.
Srabon
types of thermometer?
yemisi Reply
thermometer, Radiation thermometer and vapour pressure thermometer.liquid thermometer use thermometric liquid like mercury ,alcohol etc.
rupendra
liqid thermometer ,gas thermometer, resitance thermometer,thermo electric thermometer , radiation thermometer andvapour pressure thermometer
rupendra
calculate the quantity of heat required to rise the temperature of 1gmail of ice _10 to 110
Dargu Reply
A 40cm tall glass is filled with water to a depth of 30cm. A.what is the gauge pressure at the bottom of the glass? B.what is the absolute pressure at the bottom of the glass?
Abdulaziz Reply
A glass bottle full of mercury has mass 50g when heated through 35degree, 2.43g of mercury was expelled. Calculate the mass of the mercury remaining in the bottle
Anjorin Reply
Two electric point charges Q=2micro coulomb are fixed in space a distance 2.0cm apart. calculate the electric potential at the point p located a distance d/2 above the central point between two charges
Abdul Reply
what is wave
Ahmed Reply
A wave is a periodic disturbance which travel with a finite velocity and remains unchanged in type as it travels.
Justine
What's a wave motion?
Justine
What is charge bodies
Oje Reply
which have free elections
Usman
Show that if a vector is gradient of a scaler function then its line around a closed path is zero
Pak
Charge bodies are those which have free electons
Pak
the melting point of gold is 1064degree cencius and is boiling point is 2660 degree cenciu
Ilyas Reply
is Thomas's young experiment interference experiment or diffraction experiment or both
Ilyas Reply
An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?
eugene
A 4.0kg mess kit sliding on a fractionless surface explodes into two 2.0 kg parts.3.0 m/s due to north and 0.5 m/s 30 degree north of east. what is the speed of the mess kit
Shahid
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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