- CHAPTER 05

Magnetism andMatter

') I

,A,! I (1 "lJ1

Chapter Analysis w.r.t, Lost 3 Year's Board ExamsThe analysis given here gives you an analytical picture of this chapter and will help you toidentify the concepts of the chapter that are to befocussed more from exam point of view.

Number of Questions asked in last 3 years2015 2016 2017

Delhi All India Delhi All India Delhi I All India

Very Short Answer (1 mark) IQ IQ !!

Short Type I Answer (2 marks) i!

Short Type II Answer (3 marks) I !Long Answer (5 marks) i

Value Based Questions (4 marks) I• In 2015, there is no question was asked in both sets.• In 2016, only one question of 1marks based on Paramagnetic concepts.• In 2017 only one question of 1mark based on Earth as a Magnet was asked in Delhi set.

On the basis of above analysis, it can be said that from exam point of view Magnetic Dipoleand Earth as a Magnet are most important concepts of the chapter.

[TOPIC 1] Magnetic Dipoleand Magnetic Field Lines

A magnet is a material or an object that producesa magnetic field. The magnetic field is invisiblebut is responsible for most notable property ofmagnet.

1.1 Force Between TwoMagnetic Poles

Magnitude of force acting between two magneticpoles is given by

-m1 +m2

~ EI---r----+l1

F =k&... m,m2

41t r2

where, m, and m2 are magnetic strength of polesand k is magnetic force constant.Its SI unit is A-m.

Magnetic Field LinesThese are imaginary lines which give pictorialrepresentation for the magnetic field inside andaround the magnet.

B

Their properties are given as below:(i) These lines form continuous closed loops.

(ii) The tangent to the field line gives directionof the field at that point.

(iii) Larger the density of the lines, stronger willbe the magnetic field.

(iv) These lines do not intersect one another.

1.2 Magnetic DipoleAn arrangement of two equal and oppositemagnetic poles separated by a small distance.e.g. A bar magnet.

Magnetic Dipole Moment (M)It represents the strength of magnets. Themagnetic dipole moment of a magnetic dipole isgiven by M = m x 2 Iwhere, m is pole strength and 21 is 1m +1dipole length directed from S to N. S - N

The SI unit of magnetic dipole I+-- 21-----+l

moment is A_m2 or J{f. It is a vector quantity andits direction is from South pole to North pole.

Magnetic field strength at a point due to abar magnet at

(i) on axial line (end-on-position)

B = &... 2 M (.,'r» n• 41t rl

The direction of magnetic field is along thedirection of magnetic dipole moment (M).

(ii) on equatorial line (broadside-on-position)B = _ 1:.2.. M = _ Il oM

t 41t rl 41tr3

IBNI

II Be

Equatorial, a I +line \ : ~

\ I ~Bs: x

Ir ~! ~II

s I

~ NM

I' 21-,..--1

CHAPTER 5 : Magnetism and Motter

The direction of magnetic field is parallel tothe magnetic dipole and opposite to thedirection of dipole moment.

1.3 Torque on a BarMagnet in a Uniform.Magnetic Field

A uniform magnetic field B is represented byequidistant parallel lines, NS is a bar magnet oflength 21and strength of each pole is M.

Torque, 't = MB sin 9 =M x B

q~~t~t:(a) 't=M x B

(b)

where, 9 is the angle between M and B. Its SIunit is joule per tesla (JT1).

'tmax = MB, when dipole is perpendicular to thefield and 't = 0, when dipole is parallel oranti-parallel to the field.

Potential Energy of a MagnetDipole (Bar Magnet) in aMagnetic fieldPotential energy of a magnetic dipole in amagnetic field is given by

u= - MBcos9 = -M·B

where, e is the angle between M and B.Work done in rotating the dipole in a uniformmagnetic field from 91 to 92 is given by

W = ME (cos 9) - cos 92)

The direction of dipole moment can be obtainedby right hand thumb rule. Its SI unit is A-m2.

NorE Current loop behaves like a magnetic dipole whosedipole moment is given by

M=IA

167

1.4 Magnetic Dipole MomentMagnetic dipole moment of a revolving electron isgiven by

M = evr or M = _e_L2 2m

where, v is the speed of electron on a circular pathof radius r. L is angular momentum and given asL = mvr.

L

mOrbital magnetic moment

of a revolving electron

Mutual InteractionMutual interaction between two magnetic dipoles isF=h. 6m1m2

41t r4

where, m1 and m2 are magnetic strength of poles oftwo different magnets.

Oscillation of a Freely SuspendedMagnetThe oscillations of a freely suspended magnet(magnetic dipole) in a uniform magnetic field areSHM. The time period of oscillation,

T = 21t~ I = 21tME c.o

where, I = moment of inertia of the magnet,M = magnetic moment andB = magnetic field intensity.

Bar Magnet as an EquivalentSolenoidThe expression of magnetic field at distance r fromcentre is given by

B=J:I:2... 2M41t r3

This expression is equivalent to that of bar magnet.

168 o Chopterwise eBSE Solved Papers: PHYSICS

1.5 The Electrostatic AnalogueThe magnetic dipole is analogous to an electricdipole consisting of two equal charges of oppositesign (±q) seprated by a certain distance (2a). It has anelectric dipole momentic p = q(2a)The Dipole Analogy

Free Space ConstantElectrostatics Magnetism

(1/ Eo> ( lio>

Dipole moment p M

Equatorial field for a short - p/47tEor3 -!1oM/47tr3dipoleAxial field for a short dipole 2p /47tEor3 !102M/47tr3

External field: Torque pxE MxB

External field : Energy -p·E - M·B

Magnetism andGauss'Law

LlS

The net magnetic flux «Ps)through any closed surface isalways zero.This law suggests that thenumber of magnetic field lines leaving any closedsurface is always equal to the number of magneticfield lines entering it.

(Ps=~B·~S=O=fsK~S=O

PREVIOUS YEARS'EXAMINATION QUESTIONSTOPIC 1o 2 Marks Questions

1. Draw the magnetic field lines due to acurrent passing through a long solenoid.

B

Use Ampere's circuital law, to obtainthe expression for the magnetic fielddue to the current I in a long solenoidhaving n number of turns per unitlength.Delhi 2014C

2. A circular coil of N turns and radius Rcarries a current 1. It is unwound andrewound to make another coil of radiusR/2, current I remaining the same.Calculate the ratio of the magneticmoments of the new coil and theoriginal coil. All India 2012

3. A circular coil of N turns and diameterd carries a current 1. It is unwound andrewound to make another coil ofdiameter 2d, current I remaining thesame. Calculate the ratio of themagnetic moments of the new coil andthe original coil. All India 2012

4. Explain the following:(i) Why do magnetic lines of force

form continuous closed loops?(ii) Why are the field lines repelled

(expelled) when a diamagneticmaterial is placed in an externaluniform magnetic field? Fareign 2011

5. A small compass needle of magneticmoment M and moment of inertia I isfree to oscillate in a magnetic field B. Itis slightly disturbed from itsequilibrium position and then released ..Show that it executes simple harmonicmotion. Hence, write the expression forits time period. HOTS; Delhi 2011C

6. How does a circular loop carryingcurrent behaves as a magnet?Delhi 2011

7. Deduce the expression for the magneticdipole moment of an electron orbitingaround the central nucleus.All India 2010; Fareign 2009

o Explanations1.

Q

~;,;:';Ef~0!;;;",~Applying Ampere's circuital law for therectangular loop abed,

pB. dl = !.Lol

PB .dl = J.~'dl + JbB. dl + L'h. dl + J,' dl

but JbB.d1 = J'.dl = Bdlcos90o= O.

df B . dl = 0 as B = 0c rn

[for points outside the solenoid]

:. pB. dl= BJ: dl = Bl

Total current threading the loop abed = nIlBh = !.Lol(nh)

::} B = !.Lonl (1J

2. The length of wire will be same in two cases asthe same coil is unwound and rewound.

Length of the wire is same

.. N; x (27tR) = N2 X 27t (%)[Nj and N 2 = number of turns in two coils]

~=~ ~~Now, the ratio of magnetic moments is given by

Mj _ N, I Aj _ Nj x 7tRf

M2 - N2l A2 - N2 x 7tR~

Mj _ (Nj) (R)2M2 - 2Nj x R/2

=~X4=22 ~~

Mj : M2 = 2: 1 (1I2J

3. The length of wire will be same in two cases as thesame coil in unwound and rewound.Length of wire of coil l = Length of wire of coil 2

N; x nd, = N2 X 7td2

N; X 7td=N2 X 1t X 2d

N2=Nj2

? N2 .u, =1: 2::} Nj:N2=2:1

Magnetic moment, M = NIA

(1/2)

(1)

[where, N, = N]

(1I2J

(1I2J

::}

Mj = Njl Aj = Nj7tdz

M2 N2l A2 N21t(2d) 2

Mj = (Nj ) x .!. = 2 x .!. = ~M2 N2 4 4 2

Mj =~M2 2

Mj : Mz =1: 2 (112)

(112)

4. (i) Magnetic lines of force come out from Northpole and enter into the South pole outside themagnet and travels from South pole to Northpole inside the magnet. So, magnetic lines offorce form closed loop, magnetic monopoles donot exist. (1)

(ii) The diamagnetic material gets slightlymagnetised in a direction opposite to externalfield, therefore lines of force are repelled bydiamagnetic material. (1)

.NOTE When South pole of the magnet is viewed with the frame ofreference inside the magnet would appear as North pole andsimilarly, North pole as South pole. Therefore, magnetic linesof force traversed from South pole to North pole inside themagnet.

170 o ehapterwise eBSE Solved Papers PHYSICS

5. As the needle is displaced from the equilibriumposition, the torque will try to bring it back inequilibrium position hence, acceleration will berelated with negative of angular displacement.

When compass needle of magnetic moment Mand moment of inertia I is slightly disturbed byan angle 9 from the mean position of equilibrium.Then, restoring torque begin to act on the needlewhich try to bring the needle back to its meanposition which is given by

t = - MB sin 9Since, 9 is smallSo, sin9 = 9.. t=-MB9But t = Iawhere, a = angular acceleration

M =magnetic moment of dipoleOn comparing Eqs. (i) and (ii).

~ Ia = - MB9 ~ a = - (~B)9

.. aoc-9~Angular acceleration oc - angulardisplacement~ Therefore, needle executed SHM.Hence, the time period,

T= ': = fT or T="~

... (i)... (ii)

(1)

(1)

This is the required expression.

6. The current round in the face of the coil is inanti-clockwise direction, then this behaves like aNorth pole, whereas when it viewed from otherscale, then current round in it is in clockwisedirection necessarily forming South pole of

(1)

Hence, current loop have both magnetic poles andtherefore, behaves like a magnetic dipole. (1)

As we know that a moving charge alwaysproduces an electric current, so there will beelectric current due to revolving electron, this isthe current which produces magnetic field.

7.

Let an electron revolves around the nucleus on acircular path of radius r with a uniform linearspeed v.

Time period of electron is given byT = 21tr

v:. Electric current produced due to the orbitalmotion of electron is given by

1= Charge = -eTime T

I=~

(2~r)

I=-~21tr

Magnetic dipole moment is given by

M = lA = (;; )1tr2

M = _ evr2

M=-~(mvr)2m

where, m = mass of electron.M = __e_L

2m

... (i)(1)

where, L = mvr and known as angular momentum,

M = - _e_L2m

The direction of magnetic dipole moment isperpendicular to the plane of paper and directedinward. (1)

[TOPIC 2] Earth's Magnetism and MagneticProperties of Material

2.1 Earth as a MagnetEarth behaves like a magnet whose North poleis somewhere close to geographical South poleand magnetic South pole is closed togeographical North pole.

IE------,''--..:\-+-~ Geographic equator

Sg '\The circulating ions in the highly conductingearth's core form current loops and which inturn produces magnetic field.

2.1 Magnetic ElementsThere are three elements of the earth magnefield namely

(i) The angle between geographical meridianand magnetic meridian at a place isknown as angle of declination (a).

Vertical

Geographic t Woa.9/-\e\ICmeridian ! ..ne(i01a.(\

Ilg I"

Ng

Nm ..... • --~---,: .-- ---6ip.- ': ··..... angle

B Ilm

Determination of declaration at a place

(ii) Magnetic Inclination or Dip In magneticmeridian, the angle made by direction of theearth's total magnetic field (Be) with thehorizontal is known as dip (0).

(iii) Horizontal component of the earth'smagnetic field, It is the component of theearth's magnetic field along the horizontaldirection. He = Be cos 0

Geographic l">meridian

Magneticmeridian

C 0• Relationship between horizontal and vertical

components of the earth's magnetic field andangle of dip is given by

He = Be cos 0

Ve';"B(sinO => ~=tanoHe

Various Terms Related toMagnetismMagnetic Intensity (H)The capability of magnetic field to magnetise thesubstance is measured in terms of magnetic intensityof the field.

BH=--.!!.

Ilowhere, Bo = magnetic field inside vacuum andIlo = 41t X10-7 T-mA -1.

Its SI unit is Am-I.

172

Intensity of Magnetisation (I)The magnetic dipole moment induced per unitvolume in the field of specimen of magneticmaterial in magnetising field is known asintensity of magnetisation.

M mI=-=~

V Awhere, M = magnetic dipole moment,

m == pole strength,V = volume of specimen

and A = cross-sectional area.

Magnetic Inductor (B)The resultant magnetic field produced inside thespecimen of magnetic material aftermagnetisation is known as magnetic inductor.

Magnetic Permeability (J..l)It is equal to the ratio of magnetic induction tomagnetising field

B~= H

Magnetic Susceptibility (Xm) It is equal tothe ratio of intensity of magnetisation and

.. fl ld Imagnensmg ie Xm =-H

o Chapterwise CBSE Solved Papers PHYSICS

It has no unit. It is a scalar quantity.

Magnetic Induction [BJIt is defined as the total number of magnetic linesof force crossing per unit area through the magneticmaterial.

B = ~o (H + 1) = ~oH(l + Xm)

where, ~o = permeability of free space,H = magnetising field

and I = intensity of magnetisation.The 51 unit of magnetic induction is Tesla(T) orwbm"? which is equivalent to Nm-1A -lor JA -lm-2

2.4 Classification ofMagnetic substance

On the basis of mutual interactions or theirbehaviours, the magnetic materials placed in auniform magnetic field are classified into threeparts.

(i) Paramagnetic substance(ii) Diamagnetic substance

(ill) Ferromagnetic substance

Property Paramagnetic substance Ferromagnetic substanceDiamagnetic substanceWhen placed in auniform magneticfield

Feebly magnetise alongapplied field

Feebly magnetise oppositeto magnetic field orrepelled by magnets

Strongly magnetise alongmagnetic field

Susceptibility (xJ Very large Xm> 1000Small and positive0< Xm< E,E = small number

Small and negative-I <Xm<O

Relative permeability 1 <llr<I+EE = small number

Large value Il r > 1000Positive and less than oneO<llr<1

Effect of temperature Independent withtemperature

1X oc -- (T> T.e)

m T- Te

linearly change Linear change and Non-linear change andsaturable low temperature ultimately attains

saturationTends to move from weaker Tends to move from Tends to move quicklyto stronger magnetic field stronger to weaker from weaker to stronger

___ mag~c:.t!_~!i:_~~ ~_a..~!:~!i~_!~~~~ _Pb, Hp, NaCl, Bi, Cu, si, Sb Na, cs. 02' CuCI2, Al Ni, Co, Fe, Fep Jo Gd

Variation of IwithH

In a non-uniformmagnetic field

Examples

CHAPTER 5 : Magnetism and Motter

Curie Law

iIt states that the magneticsusceptibility of paramagnetic Xsubstances is inverselyproportional to absolute

. Itemperature, i.e. X ee -T

For paramagnetic material,CX=-T

Curie TemperatureWith the rise of temperature, susceptibility offerromagnetic materials decreases. At a certaintemperature, ferromagnetic pass over toparamagnetic. This transition temperature iscalled Curie temperature.

---+ T

[C = Curie constant]

Curie-Weiss LowThis describes the magnetic susceptibility Xm ofa ferromagnet in the paramagnetic region abovethe Curie point. It is expressed as

CX [·:T>Tc]

m = T - Tc

where, C is called Curie's constant. T is an absolutetemperature in kelvin and Tc is Curie temperature.

1.4 Permanent Magnetsand Electromagnets

The substance which at room temperature retaintheir ferromagnetic property for a long period oftime are called permanent magnet.Permanent magnet can be made by placing a rodof ferromagnetic material in a current carryingsolenoid. The magnetic field of the solenoidmagnetises the rod. The material used for makingpermanent magnet should have high retentivity,so that the magnetisation is strong and highcoercivity so that the magnetisation is not erasedby stray magnetic field/temperature fluctuationsor minor mechanical damage. Steel is favouredfor making permanent magnet.• Steel possesses high coercivity, hysteresis loss,

moderate permeability, susceptibility andretentivity, therefore it is fit for makingpermanent magnet.

173

• On placing a soft iron rod in a current earringsolenoid the magnetism of the solenoidincreases by thousards folds. On switching offthe solenoid current the magnetism is effectivilyswitch off. It is because the soft iron core has alow retentivity.

Some suitable materials for making permanentmagnets are alnico, cobalt, steel and ticonal.• Soft iron possesses high permeability,

susceptibility, retentivity and low coercivity ahysteresis loss, therefore it is fit for makingelectromagnet.

PREVIOUS YEARS'EXAMINATION QUESTIONSTOPIC 2o 1 Mark Questions

1. At a place, the horizontal component ofearth's magnetic field is B and angle ofdip is 60°. What is the value of horizontalcomponent of the earth's magnetic field atequator? Delhi 2017

2. In what way is the behaviour of adiamagnetic material different from thatof a paramagnetic, when kept in anexternal magnetic field? All India 2016

3. Relative permeability of a materialu, = 0.5. Identify the nature of themagnetic material and write its relation ofmagnetic susceptibility. Delhi 2014

4. What are permanent magnets? Give oneexample. Delhi 2013

5. Where on the surface of earth is thevertical component of earth's magneticfield zero? Delhi 2013C; All India 2011

. 6. The horizontal component of the earth'smagnetic field at a place is B and angle ofdip is 60°. What is the value of verticalcomponent of the earth's magnetic field atequator? Delhi 2012

7. What is the angle of dip at a place wherethe horizontal and vertical components ofthe earth's magnetic field are equal?Foreign 2012

174

8. A magnetic needle free to rotate in avertical plane orients itself vertically at acertain place on the earth. What are thevalues of

(i) horizontal component of the earth'smagnetic field and

(ii) angle of dip at this place? Foreign 2012

9. Where on the surface of earth is the angleof dip 90°? All Indio 2011

10. The permeability of a magnetic materialis 0.9983. Name the type of magneticmaterial, it represents. Deihl 2011

11. The susceptibility of a magnetic materialis 1.9X 10-5. Name the type of magneticmaterial, it represents. Delhi 2011

12. The susceptibility of a magnetic materialis - 4.2 X 10-6. Name the type of magneticmaterial, it represents. Deihl 2011

13. What is the characteristic property of adiamagnetic material? Foreign 201D

14. Define the term magnetic declination.All India 2009C

o 2 Marks Questions15. Show diagrammatically the behaviour of

magnetic field lines in the presence of(i) paramagnetic and

(ii) diamagnetic substances.How does one explain thisdistinguishing feature? All India 2014

16. Out of the two magnetic materials, A hasrelative permeability slightly greater thanunity while B has less than unity. Identifythe nature of the materials A and B. Willtheir susceptibilities be positive ornegative? Dalhl2014

17. Give two points to distinguish between aparamagnetic and diamagnetic substance.Delhl2014C

18. (i) How is an electromagnet differentfrom a permanent magnet?

o Chopterwise CSSE Solved Papers: PHYSICS

(ii) Write two properties of a materialwhich makes it suitable for makingelectromagnet. All India 2014C

19. The relative magnetic permeability of amagnetic material is 800. Identify thenature of magnetic material and state itstwo properties. Deihl 2012

20. (i) How does a diamagnetic materialbehave when it is cooled at very lowtemperature?

(ii) Why does a paramagnetic sampledisplay greater magnetisation whencooled? Explain. Delhi 2012

21. A magnetic needle free to rotate in avertical plane parallel to the magneticmeridian has its North tip down at 60°with the horizontal. The horizontalcomponent of the earth's magnetic field atthe place is known to be 0.4 G. Determinethe magnitude of the earth's magneticfield at the place. Deihl 2011

22. (i) Name the three elements of theEarth's magnetic field.

(ii) Where on the surface of the Earth isthe vertical component of the Earth'smagnetic field zero? Foreign 2011

23. Distinguish between diamagnetic andferromagnetic materials in terms of

(i) susceptibility and(ii) their behaviour in a non-uniform

magnetic field. All India 2011

24. (i) Write two characteristics of amaterial used for making permanentmagnets?

(ii) Why is core of an electromagnetmade of ferromagnetic materials?

Dalhl2D10

25. The horizontal component of the earth'smagnetic field at a place is .J3 times itsvertical component there. Find the valueof the angle of dip at that place. What isthe ratio of the horizontal component tothe total magnetic field of the earth atthat place? All India 2010C

CHAPTER 5 : Magnetism and Motter

26. The horizontal component of the earth'smagnetic field at a place equals to itsvertical component there. Find the valueof the angle of dip at that place. What isthe ratio of the horizontal component tothe total magnetic field of the earth atthat place? HOTS:All India 2010C

27. Draw magnetic field lines when a(i) diamagnetic, (ii) paramagneticsubstance is placed in an externalmagnetic field. Which magnetic propertydistinguishes this behaviour of the fieldlines due to the two substances? Delhi 2010

28. State briefly an efficient way of makinga permanent magnet. Write twoproperties to select suitable materialsfor making permanent magnets.Delhi 2009C

29. Out of the following, identify thematerials which can be classified as(i) paramagnetic (ii) diamagnetic(a) Aluminium (b) Bismuth(c)Copper (d) SodiumWrite one property to distinguishbetween paramagnetic and diamagneticmaterials. Delhi 2009C

o 3 Marks Questions30. A wheel with 8 metallic spokes each

50 cm long is rotated with a speed of120 rev/min in a plane normal to thehorizontal component of the earth'smagnetic field. The earth's magneticfield at the place is 0.4 G and the angleof dip is 60°. Calculate the emf inducedbetween the axle and the rim of wheel.How will the value of emf be affected, ifthe number of spokes were increased?All India 2013

31. Three identical specimens of a magneticmaterials nickel, antimony andaluminium are kept in a non-uniformmagnetic field. Draw the modification inthe field lines in each case. Justify youranswer. Delhi 2011

175

32. (i) What happens when a diamagneticsubstance is placed in a varyingmagnetic field?

(ii) Name the properties of a magneticmaterial that makes it suitable formaking (a) a permanent magnet and (b)a core of an electromagnet. Foreign 2009

33. (i) How does angle _of dip change as I Iline goes from . .magnetic pole to --------x-----magnetic equator :3 Eof the earth? .=::~;~=.

(ii) A uniform = ymagnetic fieldgets modified as shown in the figurebelow, when two specimens X and Yare placed in it. Identify whetherspecimens X and Yare diamagnetic,paramagnetic or ferromagnetic. Foreign

2009

34. When two materials are placed in anexternal magnetic field, the behaviour ofmagnetic field lines is as shown in thefigure. Identify the magnetic nature of eachof these two materials. Delhi 2009C------

I I ::=t:E-----x-- y

o 5 Marks Questions35. (i) A small compass needle of magnetic

moment M is free to turn about an axisperpendicular to the direction ofuniform magnetic field B. The momentof inertia of the needle about the axisis 1. The needle is slightly disturbedfrom its stable position and thenreleased. Prove that it executes simpleharmonic motion. Hence, deduce theexpression for its time period.

(ii) A compass needle free to turn in avertical plane orients itself with itsaxis vertical at a certain place on theearth. Find out the values of .(a) horizontal component of the earth's

magnetic field and(b) angle of dip at the place. Delhi 2013

o Explanations\81.

I is the total magnetic field.B BNow I cos 60° = B ~ I =--- =- =2B

, cos 60° 1/2

At equator, dip angle is 0°... BH = lcosOo= I = 2B. (1)

2. When paramagnetic materials are placed in externalmagnetic field, these are feebly magnetised in thedirection of the applied external magnetic fieldwhereas in case of diamagnetic materials, these arefeebly magnetised opposite to that of applied'external magnetic field. (1)

3. The nature of magnetic material is a diamagnetic.The relation between relative permeability andmagnetic susceptibility is

Ilr =1 + Xm (1)

4. Permanent magnets are those magnets which havehigh retentivity and coercivity. The magnetisation ofpermanent magnet is not easily destroyed even if itis handled roughly or exposed in stray reversemagnetic field, e.g. steel. (1)

5. At equator, vertical component of earth's magneticfield will be zero. (1)

6. The horizontal and vertical components of the earth'smagnetic field are perpendicular to each other.

Horizontal component of earth's magnetic field,H = B, cos 60° = B (given)

B x! = B or B, = 2B, 2Vertical component of earth's magnetic field,. J3 r:;V = B Sill 60° ~ V = 2B x - ~ V = v 3B

e 2

7. The angle of dip is given by

0= tan"! (!:)component of the earth's magneticBv = vertical

field.BH = horizontal component of the earth's

magnetic field.So, as Bv=BHThen, 0 = tan'" (1) = 45°

:. The angle of dip will be 0 = 45°.

8. (i) The coil is free to move in vertical plane, itmeans that there is no component of theearth's magnetic field in horizontaldirection, so the horizontal component ofthe earth's magnetic field is zero. (112)

(ii) The angle of dip is 0°. (112)

9. At poles, the angle of dip is 90°. (1)

10. The magnetic material is diamagneticsubstance for which Ilr < 1. (1)

11. The small and positive susceptibility of1.9 x 10-5 represents paramagnetic substance.

(1)

12. Negative susceptibility represents diamagneticsubstance. (1)

13. Diamagnetic material acquires feeblemagnetisation in the opposite direction of themagnetic field when they are placed in anexternal magnetic field. (1)

14. Magnetic declination The angle betweengeographical meridian and magnetic meridianat any place of the earth is known as magneticdeclination (ex) at that place of the earth. (1)

15. Magnetic permeability of paramagnetic is morethan air, so it allows more lines to pass through itwhile permeability of diamagnetic is less thanair, so it does not allow lines to pass through it.(l)For figure, refer page 177.

This difference can be explained asdiamagnetic substances repel or expel themagnetic field lines while paramagneticsubstance attract the magnetic field lines. (1)

16. The nature of the material A is paramagneticand its susceptibility Xm is positive.The nature of the material B is diamagneticand its susceptibility Xm is negative. (2)1~ _

(1)

Paramagneticsubstance

Diamagneticsubstance

1. A paramagneticsubstance is feeblyattracted by magnet.

A diamagneticsubstance is feeblyrepelled by a magnet.

2. For a paramagneticsubstance, theintensity ofmagnetisation has asmall positive value.

For a diamagneticsubstance, theintensity ofmagnetism has asmall negative value.

(2)

(1)

CHAPTER 5 : Magnetism and Motter

18. An electromagnet consist of a core made of aferromagnetic material placed inside a solenoid.It behaves like a strong magnet when currentflows through the solenoid and effectively losesits magnetism when the current is switched off.(i) A permanent magnet is also made up of a

ferromagnetic material but it retains itsmagnetism at room temperature for a longtime after being magnetised one. (1)

(ii) Properties of material are as below:(a) High permeability (c) Low retentivity(b) Low coercivity (1)

19. Ferromagnetic substance are those substanceswhich have very high magnetic permeability. (1)

Properties (i) High retentivity(ii) High susceptibility (Xm > 1000)

(2 x 112)

20. (i) As, the resistance (electrical of metaldecreases with decrease in temperature.But for diamagnetic substances, thevariation of susceptibility is very small(0 < Xm < f), i.e. diamagnetic materials areunaffected by the change in temperature(except bismuth). (1)

(ii) Paramagnetic materials when cooled due tothermal agitation tendency alignment ofmagnetic dipoles decreases. Hence, theyshows greater magnetisation. (1)

21. Angle of dip, 0 = 60° = ~3

Horizontal component of the earth's magneticfield, H = 0.4 GEarth magnetic field (Be) =?.: Horizontal component of the earth's magneticfield, H = B, cos 0 (1)

~ Be = ~ = 0.4 G = 0.4 G = 0.8 Gcos 0 cos 60° (~)

22. (i)

B, = 0.8 G (1)

The earth's magnetic field at a place can becompletely described by three parameterswhich are called elements of earth'smagnetic field. They are as follows:

(a) Angle of declination (8)(b) Angle of dip (0) or magnetic inclination(c) Horizontal component of earth's

magnetic field (He)At the magnetic equator, the dip needlerests horizontally, so that the angle of dip iszero at the magnetic equator.

(ii)

177

23. (i) Susceptibility for diamagnetic material It isindependent of magnetic field and temperature(except for bismuth at low temperature). (1)

Susceptibility for ferromagnetic material Thesusceptibility of ferromagnetic materials decreasessteadily with increase in temperature. At the Curietemperature, the ferromagnetic materials becomeparamagnetic.

(ii) Behaviour in non-uniform magnetic fieldDiamagnets are feebly repelled, whereasferromagnets are strongly attracted bynon-uniform field, i.e. diamagnets move in thedirection of decreasing field, whereasferromagnet feels force in the direction ofincreasing field intensity. (1)

24. (i) Two characteristics of material used formaking permanent magnets are

(a) high coerdvity(b) high retentivity and high hysteresis loss.

(2 x 112)

(ii) Core of an electromagnet made of ferromagneticmaterial because of its(a) low coerdvity(b) low hysteresis loss (2 x 1/2)

25. As vertical and horizontal components of magnetic fieldsare perpendicular to each other, when their magnitudesare equal, resultant will divide their angle equally.

According to the question, H = J3 V

where, H and V are the horizontal and verticalcomponents of the earth's magnetic field.If angle of dip at that place is 0, then

tano=~=~ [.: H=J3VJH J3v

tano=~ ~ o=~J3 6 (1)

':Horizontal component of the earth's magnetic field,H = B, cos 0where, B, = Earth's magnetic field

.!i = cos 0 = cos ~ = J3 ~ H : B = J3 :2B, 6 2 e (1)

26. Refer to Ans. 25. (Ans.l : ..[2).

27. (i) Behaviour of magnetic field lines whendiamagnetic substance is placed in an externalfield.

(2)

(1)

178

28.

Magnetic susceptibility distinguishes thebehaviour of the field lines due to diamagneticand paramagnetic substance. (1)

Permanent magnet can be made by putting a steelrod inside the solenoid and a strong current isallowed to pass through solenoid. The strongmagnetic field inside the solenoid magnetise therod. (1)

For properties to select suitable materialsfor making permanent magnetsRefer to sol. 23 (i). (1)

(i) Paramagnetic substance Aluminium, sodium (1)

(ii) Diamagnetic substance Bismuth, copper,the susceptibility of the diamagnetic materialsis small and negative, i.e. -1< Xm < 0, whereasfor paramagnetic substance the susceptibility issmall and positive, i.e. 0 < XIII < a, where a is asmall number. (1)

.,' Horizontal component,1H = Bcos e= 0.4 cos 60° = 0.4x - = 0.2G2

H = 0.2 xt 0-4 T [.,' cos 60° = 1/2]

29.

30.

This component is parallel to the plane of wheel.The wheel is rotating in a plane normal to thehorizontal component, so it will cut the horizontalcomponent only, vertical component of earth willcontribute nothing in emf. (1)Thus, the emf induced is given as

E = ~Hl2CJ)221tNwhere, CJ) = -- and

tI = length of the spoke = 50 em = 0.5 m

1 -4 2 2x314x120E=-xO.2xlO x(o.~ x----

2 60E = 3.14 X 10-5 V

31.

The value of emf induced is independent of thenumber of spokes as the emf's across the spokesare in parallel. So, the emf will be unaffectedwith the increase in spokes. (1)

The modifications are shown in the figure.

o ehopterwise eSSE Solved Papers PHYSICS

--------I I

(Vo x 3= lV2)

It happens because(i) nickel is a ferromagnetic substance.(ii) antimony is a diamagnetic substance.

(ill) aluminium is a paramagnetic substance.(Vox 3 = 1 Vi)

32. (i) When diamagnetic substance is placed in avarying magnetic field, it tends to move fromstronger magnetic field to weaker magneticfield. (1)

(ii) Refer to Ans. 18 (i) and (ii). (2)

33. (i) The angle of dip decreases from 90° to 0°. (1)(ii) For paramagnetic materials, no magnetic lines

of force enter in it. So, specimen X isparamagnetic. For ferromagnetic materials, allmagnetic lines of force prefer to go through it.So, specimen Y is ferromagnetic. (2J

34. (i) MaterialXis paramagnetic substance. When aspecimen of a paramagnetic substance isplaced in a magnetising field, the lines of forceprefer to pass through the specimen ratherthan through air. Thus, magnetic inductioninside the sample is more than the magneticintensity. (lVoJ

(ii) Material Y is ferromagnetic substance. Theseare the substances in which a strongmagnetism is produced in the same directionas the applied magnetic field, these arestrongly attracted by a magnet exhibits highlyconcentrated lines of force. (lVoJ

m 35. The torque always tries to bring back the needlein equilibrium position i.e. parallel to the existingfield.

(i) The torque on the needle is r = M x BIn magnitude, 't = MB sin eHere, r is restoring torque and e is the anglebetween M and B.Therefore, in equilibrium,Restoring force = Deflecting torque

J d~ = - MBsin edt2 (lJ

CHAPTER 5 : Magnetism and Motter

Negative sign with MB sins implies thatrestoring torque is in opposition todeflecting torque.For small values of a in radians, weapproximate sin a = a and get

ld~ = - MBadt2

d2a = _ MBadt2 I

d2a = _ o}a

dt2 (1)

This equation represents a simple harmonicmotion. The square of the angular frequency• 2 MB. 2 MBISW =-l.e.w =-

I I

=>

=>

179

where, w=~

. . d 21t g.Time peno ,T = - = 21t -ro MB (1)

(ii) (a) As, horizontal component of earth'smagnetic field, BH = B cosoPutting 8 = 90° (as compass needle orientsitself vertically)

.. BH = 0(b) For a compass needle oriented itself with its

axis vertical at a certain place, angle of dip,8 = 90°. (2)

Value Based Questions (From Complete Chapter)(21 4 Marks Questions

1. Bala and Rama (class X students), wereassigned a project based on magnetism.In their project work, they hadcalculated the value of the earth'smagnetic field. When they submittedtheir project for verification. Mr.Santosh, their Physics teacher,corrected the mistakes. He alsosuggested few books which could beuseful for them.

(i) What values did Mr. Santoshexhibit towards his students?Mention any two.

(ii) Mention the three magneticelements required to calculate thevalue of the earth.

(iii) What is the strength of the earth'smagnetic field at the surface of theearth?

Ans. (i) The values of Mr. Santosh are helping innature to get the exact value. Honesty andconcern for the students to create interestin the subject. [2)

(ii) Magnetic declination, magneticinclination and horizontal component ofthe earth's magnetic field. [1]

(iii) It is of the order oflO-5 T. [1]

2. Mr. Sairam the chief development officer, insouthern railway went on an official tour toattend a seminar on fast moving trains. Hemet his friend Onstosaki in Tokyo after hefinished his seminar there. fIis friendexplained to Sairam, how Japanese peopleare concentrating on energy conservationand saving of fossil fuels using Maglevtrains? Mr. Sairam travelled from Tokyo toOsaka in Maglev train and found that noiseis less, travelling is smooth and understoodin what way we are lagging behindJapanese in mass trasporting systems. Thisworks on the principle of Meissner's effect.

(i) What values did Mr. Sairam foundfrom Ontosaki? Mention any two.What are superconductors?What is Meissner's effect?Awareness about new technology, concern forenergy conservation, decrease of noisepollution and air pollution, i.e, concern forenvironment.

(ii)(iii)

Ans. (i)

[1)

(ii) Superconductors are the most exoticdiamagnetic materials. These are metals cooledto very low temperatures which exhibits bothperfect conductivity and perfect diamagnetism.

[2)

(iii) A superconductor repels a magnet and in turn,is repelled by the magnet. This phenomenon ofperfect diamagnetism in superconductors iscalled Meissner's effect. [1]