CLASSICAL & EARTH MAGNETISM
Magnet
Magnetic Field due to a Bar Magnet
Comparision between Electric & Magnetic Dipole
Properties of Magnetic Materials
Hysteresis : Retentivity and coerclvity
Earth Magnetism
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
full concept of magnetism, Lecture notes of Magnetic Resonance Imaging (MRI)
Magnetism is a force of attraction or repulsion that acts at a distance. It is due to a magnetic field, which is caused by moving electrically charged particles. It is also inherent in magnetic objects such as a magnet. A magnet is an object that exhibits a strong magnetic field and will attract materials like iron to it. Magnets have two poles, called the north (N) and south (S) poles. Two magnets will be attracted by their opposite poles, and each will repel the like pole of the other magnet. Magnetism has many uses in modern life.
Typology: Lecture notes
2021/2022
1 / 21
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download full concept of magnetism and more Lecture notes Magnetic Resonance Imaging (MRI) in PDF only on Docsity!
Magnet
Magnetic Field due to a Bar Magnet
Comparision between Electric & Magnetic Dipole
Properties of Magnetic Materials
Hysteresis : Retentivity and coerclvity
Earth Magnetism
Magnet :
Two bodies even after being neutral (showing no electric interaction) may attract/repel strongly if they have a special property. This property is known as magnetism. This force is called magnetic force. Those bodies are called magnets. There are two types of Magnet–
(1) Natural Magnet – These are available in nature for eg.- magnet which is available in mines is natural magnet. It has not a definite shape and size that's why this magnet is of no use for scientific and research work.Attraction power
of it is very low. (2) Artificial Magnet – These are man made magnet. Generally these are made by Fe, Al, Ni. Shape and size are
definite and attraction power is controlled by manufacturer. This is why these are used in scientific work. Generally the word "Magnet" is use for artificial magnet. Some types of artificial magnet are given below
(1) Rod/bar magnet (2) Magnetic needle (3) Slab magnet (4) Ring magnet Properties of Magnet
(1) Magnet attracts iron
(2) A freely suspended magnet remains in north-south direction always (3) There is a attraction between two unlike poles and repulsion between like poles (4) A magnet develope magnetism in magnetic elements by induction
(5) No monopole exist in real time means no south pole or north pole can exist independently. Bar magnet - A bar magnet is a rod shaped metal object which produces magnetic field in its surrounding and at the
two ends of it there are two magnetic poles – North Pole and South Pole. Magnetic lines originate from north pole of a magnet and terminate on south pole as shown in figure.
Note : Current carrying solenoid acts as a bar magnet. Magnetic poles - A magnet has two poles. If a magnet is placed within powder of iron than we get two points such that attraction force is maximum, these points are known as magnetic poles. Strength of poles depends upon the attraction. Magnetic Axis – An imaginary line which join both poles of a magnet is known as magnetic axis. Effective length of Magnet : Distance between two poles of a magnet is known as its effective length. This is measured along the magnetic axis. This length is equal to 5/6 of its geometric length. Pole strength : The efficiency by which a pole attracts magnetic substance is known as pole strength. In a magnet pole strength is increases as number of magnetic field lines increases. This is represented by
m p FBMagnetic forceMagnetic field
Unit of pole strength is ampere meter or newton/tesla.
CLASSICAL & EARTH MAGNETISM
Magnetic length :
Distance between two poles of a bar magnet known as magnetic length of a magnet Magnetic length is a vector which shows direction from south pole to north and it is represented by
2 l Magnetic length of a magnet is always less then its geometric length. All structures which show a tendensy to rotate in direction of magnetic field known as magnetic dipole A magnetic dipole can not be represented by two isolated poles becuase a single pole of magnet does not exist. Magnetic dipole moment : Multiplication of magnetic length and pole strength is known as magnetic dipole moment (^) M m( 2 )
Its a vector quantity which is a direction from south to north.
Dividing a rectangular bar magnet - Suppose we have a rectangular bar magnet having length, breadth and mass as L, b and w respectively. If it is cut in p equal parts along the length as well as perpendicular to the length it is cut in q equal parts simultaneously as shown in the figure then -
L
L'
b'
b
Length of each part L ' Lq, breadth of each part (^) b b ' (^) q , mass of each part w^ '^ ^ pqw,
pole strength of each part m^
m ' (^) p, magnetic moment of each part (^) M m L m p
L
q
M
' ' ' (^) pq.
Magnetic field due to a bar magnet - (i) End side on position, tan A Position or axial points : At point P intensity of magnetic field is N S +m –m
lm BN BS
r
B Mr r
r
0 4 2 2 2
e j
Where M = 2ml = Magnetic dipole moment
For small dipole ( r >>>> 2l)
B M
r
4 ^023
Note : Magnetic field on axial points is in the direction of magnetic moment
M.
(ii) Broad side on position or Equatorial or tan B Position :-
B = (^2 )
0 (^2 2 2 )
m r r
e j
B M
r
0
4 e 2 2 j^32
If a magnet is very small ( r >>>> 2l)
B 4 ^0 M r 3
Note : Magnetic field on equitorial points is in the opposite direction of magnetic moment
M.
Gauss's Law in Magnetism - In electrostatic electric field can be generate due to a single charge, but magnetic field can only be developed when there is a dipole because there is no existence of single pole.
Gauss’s Law for Magnetism
B ds s
z. ^0
Gauss Law proves that magnetic poles of a magnet are equal and in opposite nature, and remains always in pair.
Comparision between Electric and Magnetic Dipole
S.No. Physical Quantity to be Electric Dipole Magnetic Dipole Compared
- Dipole moment p = q (2l) M = m (2l)
- Direction of dipole moment From negative charge to the From south to north pole positive charge
- Net force in uniform field 0 0
- Net torque in uniform field ^ p^ E ^ M^ B
- Field at far away point on the axis 41 2 0 3 . (^) r p (along p ) 4 ^0.^2 r 3 M (along (^) M )
- Field at far away point on 4 1 0 3 . (^) rp (opposite p ) 4 0. M 3 r
(opposite (^) M )
perpendicular bisector
- Potential energy U = – ^
p E. (^) = – pE cos U = –
M. B= –MB cos
- Work done in rotating the dipole W 1 2 = pE (cos 1 – cos 2 ) W 1 2 = MB(cos 1 – cos 2 )
Note : In the table is the angle between field (
E or^
B ) and dipole moment (^ p or M ).
Ex.5 Figure shows two identical magnetic dipoles a and b of magnetic moments M each, placed at a separation d, with their axes perpendicular to each other. Find the magnetic field at the point P midway between the dipoles.
S N
S
N
b
d
a
(a)
S N
S
N
b
d
a
(b)
Bb
Ba
Sol. The point P is in end-on position for the dipole a and in broadside-on position for the dipole b. The magnetic field at P due
to a is B M a (^) d
4 ^023
b / 2 g
along the axis of a, and that due to b is B M b (^) d
4 ^023
b /^2 g
parallel to the axis of b as shown in
figure. The resultant field at P is, therefore.
B B (^) a^2 Bb^2 =
(^03) 4 2
M
bd / g 1 2
M
d The direction of this field makes an angle a with Ba such that tana = Bb/Ba = 1/2.
_______________________________________________________________________
Try yourself...
- A magnet of magnetic moment 50 i A-m^2 placed along x-axis. Where magnetic field is
B (^) e0 5. i 3 0. jj tesla. The torque acting on magnet is - (1) 175 (^) k N-m (2) 150 (^) k N-m (3) 75 (^) k N-m (4) (^25 37) k N-m
- Two/three/four identical bar magnets of magnetic moment 'M' are combined according to figure. Find net magnetic moment of the system -
(a) (b) (c)
(d) (e) (f)
- Magnetic field at axial point due to a short bar magnet at distance r is euqal to
B. Then the magnetic field due to this bar magnet at a distance of r/2 on it's equitorial axis -
(1)
B
B
2 (3) 4^
B (4) – 4
B
- Figure shows a small magnetised niddle P placed at a point O. The arrow shows the direction of its magnetic moment. The other arrows shows different position (and orientations of the magnetic moment) of another identical magnetised needle Q. (a) In which configuration is the system is not in equilibirum. (b) In which configuration is the system in stable and unstable equilibirum. (c) Which configuration corresponds to the lowest potential energy among all the configurations shown.
Q 4
Q 5 Q 3
Q 1 Q 2
Q 6
O P
- A magnet of magnetic dipole moment 1 × 10^4 J/T is released in a uniform magnetic field of induction 4 × 10–5^ T from the position shown in the figure. Find -
B
M
(i) Its kinetic energy at = 90° (ii) Its maximum kinetic energy during the motion. (iii) Wii it perform SHM? oscillation? Periodic motion? What is its amplitude?
Ans. 1. (2), 2. (a) 2M, (b) Zero, (c) 2 M, (d) M, (e) Zero, (f) 2 2 M, 3. (4),
- (a) PQ 1 and PQ 2 , (b) PQ 3 , PQ 6 stable and PQ 5 , PQ 4 unstable, (c) PQ 6
- (a) 0.2 J, (b) 0.6 J, (c) Oscillatory and periodic motion with amplitude of 120°
_______________________________________________________________________
(A) (B)
When no field is applied On application of field (
B )
(3) Ferro-Magnetic Substances : Ferromagnetic substances are those which gets strongly magnetised when placed in an external magnetic field. They have strong tendency to move from a region of weak magnetic field to strong magnetic field, i.e., they get strongly attracted to a magnet. The individual atoms (or ions or molecules) in a ferromagnetic material possess a dipole moment as in a paramagnetic material. However, they interact with one another in such a way that they spontaneously align themselves in a common direction over a macroscopic volume called domain. Each domain has net magnetisation. Typical domain size is 1 mm and the domain contains about 10^11. In the absence of external magnetic field domains are randomly oriented and magnetisation varies randomly from domain to domain and there is no bulk magnetisation. In the presence of external magnetic field B 0 the domains oriented in the direction of B 0 grow in size so a net large magnetisation is produced in the direction of external magnetic field. Examples - iron, aluminium, nickel, cobalt etc.
(A) Unmagnetised (B) Magnetised Methods of Magnetisation– The process by which some magnetised material such as iron, steel are converted into magnet is known as magnetisa- tion. (i) By rubbing : In this process when a magnet is rubbed again and again on a magnetic material then the material changed into a magnet. (ii) By electric current : In this process, when some copper wire are wrapped around a magnetic material and a current is provided in the wire, then the material changed into a magnet. Electro Magnet The magent which are built up with the help of electric current is known as electromagnet. For example — when a current is provided in a solenoid, then the solenoid will behaves as a magent. These are temporary magnet. When a soft iron rod is placed within a solenoid, then magnetism of solenoid increases by hundred of times.
Intenstiy of magnetisation (
I ):
When a ferromagnetic material is placed in a magnetic field, it acquires a magnetic dipole moment M. This magnetic dipole moment per unit volume of the substance is known as intensity of magnetisation. It is given by I MV
where V is the volume of the ferromagnetic specimen. If m is the pole strength developed in the specimen and 2 (^) is the magnetic length of the specimen, then
I mA 22 mA
where A is the cross-sectional area of the specimen. SI unit of intensity of magnetisation is A m–1.
Magnetic Intensity or Magnetic Field Strength ( (^) H ) When a substance is placed in an external magnetic field, it becomes magnetised. The actual magnetic field inside the substance is the sum of the external field and the due to its magnetisation. The capability of the magnetising field to magnetise the substance is expressed by means of vector ( (^) H ) , called the magnetic intensity' of the field. It is defined
through the vector relation.
B 0 H
Inside a material having magnetic permeability r the relation is modified as B 0 rH
Relation between (^) B , (^) H in I and in Magnetization of Materials is given by
B B 0 Bi B 0 H 0 I(^
H ) =
B I
where ( (^) B ) is magnetic field induction inside the substance and I is the intensity of magnetisation and 0 is the permeability of space. The SI unit of ( (^) H ) is same as of I , that is, ampere/metre (Am–1). The C.G .S. unit is oersted.
Relative magnetic permeability Relative magnetic permeability of a material is defined as the ratio of the number of lines of magnetic induction per unit area (i.e., flux density B) in the material to the number of magnetic lines per unit area that would be present it the medium were replaced by a vacume (i.e., flux density B 0 ).
r B^ B 0 Relative magnetic permeability of a material may also be defined as the ratio of magnetic permeability of the material () and the magnetic permeability of free space ( 0 ).
(^) r 0 or^ ^ ^ r^0 For diamagnetic substance r < 1 For paramagnetic substance r > 1 For ferromagnetic substance r >> 1
Property Cause of magnetism Explanation of magnetism
Behaviour in a non-uniform magnetic field
State of magnetisation
When the material in the form of liquid is filled in the U-tube and placed between pole pieces.
The value of magnetic induction B Magnetic susceptibility Dependence of o n temperature
Relative Permeability (r) Intensity of magnetisation (I)
I-H curves
Magnetic moment (M) Examples
Diamagnetic substances Orbital motion of electrons On the basis of orbital motion of electrons These are repelled in an external magnetic field, i.e,. have a tendency to move from high to low field region.
N S
Pushed up
These are weakly magnetised in a direction opposite to that of applied magnetic field Liquid level in that limb gets depresed
Liquid
N S
B < B 0 (whe re B 0 is the magnetic induction in vacuum) Low and negative || 1 Does not depend on temperature (except Bi at low temperature) x
T
r < 1 I is in a direction opposite to that of H and its value is very low
H
–I
Very low ( 0) Cu, Ag, Au, Bi, Sb, NaCl, H 2 O air and diamond etc.
Paramagnetic substances Spin motion of electons On the basis of spin and orbital motion of electrons These are feebly attracted in an external magnetic field i.e., have a tendency to move from low to high field region.
N S
Pulled in
These get weakly magnetised in the direction of applied magnetic field Liquid level in that limb rises up
Liquid
N S
B > B 0 Low but positive 1 On cooling, these get converted to ferromagnetic materials at Curie temperature x
T
r > 1 I is in the direction of H but value is low
H
+I
Very low Al, Mn, Pt, Na, CuCl 2 , O 2 and crown glass
Ferromagnetic substances Formation of domains On the basis of domains formed These are strongly attacted in an external magntic field, i.e., they easily move from low to high field region.
N S
Very strong pull
These get strongly magnetised in the direction of applied magnetic very much Liquid level in that limb rises up very much
Liquid
N S
B >> B 0 Positive and high 102 These get converted into paramagnetic materials at Curie temperature x
TC^ T
r >> 1 r = 10^2 I is in the direction of H and value is very high.
TC T
x
Very high Fe, Co, Ni, Cd, Fe 3 O 4 etc.
Comparision between Different Magnetic Materials
Hysteresis : Retentivity and coercivity :
Hystersis curve : When a ferromagnetic substance is placed in a magnetic field, it is magnetised by induction. If we vary
magnetic intensity H of the magnetising field, the intensity of magnetisation I and the flux density B in the (ferromagnetic)
substance do not vary linearly with H. In other words the susceptibility m (= I/H) and the permeability = (= B/H) of the
substance are not constants, but vary with H and also depend upon the past history of the substance.
A
O F H
C
– H
B
I or B
Coe
rciv
ity E
I or B Hysteresis Loop
D
Rem
nan
t Mag
netis
m
The variation in I with variation in H is shown in above figure. The point O represents the initial unmagnetised state of
the substance (I = 0) and a zero magnetic intensity (H = 0). As H is increased, I increase (non- uniformly) along OA. At
A the substance acquires a state of magnetic saturation. Any further increase in H does not provide any increase in I.
If now the magnetising field H is decreased, the magnetisation I of the substance also decrease following a new
path AB (not the original path AO). Thus I lags behind H. When H becomes zero, I still has a value equal to OB. The
magnetisating remaining in the substance when the magnetising field is reduced to zero is called the "residual
magnetism". The power of retaining this magnetism is called the "retentivity" or the remanence of the substance.
Thus, the retentivity of a substance is a measure of the magnetisation remaining in the substance when the magnetising
field is removed In figure OB represents the retentivity of the substance.
If now the magnetising field H is increased in the reverse direction, the magnetisation I decrease along BC, still
lagging behind H, until it becomes zero at C where H equals OC. The value OC of the magnetising field is called the
"coercive" or "coercivity" of the substance. Thus, the coercivity of a substance is a measure of the reverse magnetising
field required to destroy the residual magnetism of the substance. As H is increased beyond OC, the substance is
increasingly magnetised in the opposite direction along CD, at 0 the substance is again magnetically saturated.
By taking H back from its maximum negative value (through zero) to its original maximum positive value, a symmetrical
curve DEFA is obtained. At points B and E where the substance is magnetised in the absence of any external magnetising
field , it is said to be a "permanent magnet".
(ii) Electromagnets : The material for the cores of electromagnets should have high permeability (or high susceptibility), specially at low magnetising fields, and a low retentivity. Soft iron is suitable material for electromagnets. (iii) Transformer cores and telephone diaphragms : In these cases the material goes through complete cycles of magnetisation continuously The material must therefore have a low hysteresis loss to have less dissipation of energy and hence a small heating of the material (otherwise the insulation of wind ings may break), a high permeability (to obtain a large flux density at low field) and a high specific resistance (to reduce eddy current loses). Soft -iron is used for making transformer cores and telephone diaphragms : More effective alloys have now been developed for transformer cores. They are permalloys mum metals etc.
_______________________________________________________________________
Examples ...
Ex.1 A solenoid of 500 turns/m is carrying a current of 3A. Relative permeability of core material of solenoid is 5000. Determine the magntidues of the magnetic intensity, magetization and the magnetic field inside the core - Sol. Magnetic intensity H = I = 500 m–1^ × 3A = 1500 Am– r = 1 + , i.e. = 5000 – 1 = 4999 Hence, the magnetisation I = H = 7.5 × 10^6 Am– The magnetic field B = 0 rH = 5000 × 4 × 10–7^ × 1500 = 9.4 T Ex.2 A rod of magnetic material of cross-section 0.25 cm^2 is located in 4000 A/m magnetising field. Magnetic flux passes through the rod is 25 × 10–6^ Wb. Find out for rod - (i) permeability (ii) magnetic susceptibility (iii) magnetisation
Sol. (i) Magnetic flux = BA B = /A = (^) 0 25^25
6 4
. = 1 Wb/m^2 B = H = (^) HB = 40001 = 2.25 × 10–4^ Wb/A-m
(ii) r = 1 + m m = r – 1 FHG ^ r IKJ 0
m =
0 – 1 =^
4 7
F HG^
I KJ
= 199 – 1 = 198 (iii) Magnetization I = m H = 198 × 4000 = 7.92 × 10^5 A/m
Ex.3 In a region at 280 K temperature magnetic susceptibility of an aluminium sample is 2.4 × 10–5^ , then calculate its magnetic susceptibility 320 K -
Sol.
m m
T
T
1 2
2 1
(^) m2 = m1 × (^) TT^1 2 ^ m2^ = 2.4 × 10
–5 (^) × ^ m m
1 2
320 = 2.1 × 10–
Ex.4 A piece of iron of mass 8.4 kg is repeatedly magnetised and demagnetised by an external periodic time varying magnetic field of frequency 50 Hz. In the iron piece it is measured that rate of heat dissipation is 6.4 × 10^4 J/hr. If iron density is 7200 kg/m^3 find the energy dissipated in iron piece per cycle per unit volume of it. Sol. The heat dissipation in the iron piece per unit volume per hour is given as
Q = (^) VolumeHeat = (^) 8 46 4 720010
.^4
(^) J/hr-m 3
Period of one cycle of magnetisation is given as
T = (^1) f = (^50) ^1 3600 hr Thus heat dissipated per cycle per unit volume is given as
Qv = (^) 8 46 4 720010
.^4
× 1
50 3600 = 305 J/m
3
_______________________________________________________________________
Try yourself...
- The magnetic materials having negative magnetic susceptibility are -
(1) Non magnetic (2) Para magnetic (3) Diamagnetic (4) Ferromagnetic
- A solenoid has has 10^3 turns per unit length. On passing a current of 2A, magnetic induction is measured to be
4 Wb/m^2. Calculate magnetic susceptibility of core - (1) 4999 (2) 2999 (3) 3999 (4) 1099
- A magnetising field of 1600 A-m–1^ produces a magnetic flux of 3.14 × 10–5^ waber in a bar of iron of cross section
0.2 cm^2. Permeability of the bar will be - (1) 9.8 × 10–5^ Waber/A-m (2) 9.8 × 10–4^ Waber/A-m (3) 1.8 × 10–4^ Waber/A-m (4) 9.8 × 10^4 Waber/A-m
- An iron rod of cross sectional area 4 cm^2 is placed with its length parallel to a magnetising field 1600 Am–1. The flux
through the rod is 4 × 10–4^ weber. Find out permeability of the material of the rod? (1) 62.5 × 10–3^ Waber/A-m (2) 0.625 × 10–3^ Waber/A-m (3) 6.25 × 10–3^ Waber/A-m (4) 625 × 10–3^ Waber/A-m
- Which of the following relations is not correct -
(1) B = 0 (H + I) (2) B = 0 H (1 + m) (3) 0 = (1 + m) (4) r = 1 + m
Ans. 1. (3), 2. (1), 3. (2), 4. (2), 5. (3)
_______________________________________________________________________
Elements of the Earth's Magnetism :
- Angle of declination () : At any place angle between geographical meridian and magnetic meridian is known as angle of declination. This is an acute angle.
-is angle of declination
- Angle of dip () :
When a freely suspended dip needle remains in magnetic meridian, it makes an angle with horizontal. In this condition, angle made by magnetic axis with horizontal is known as angle of dip. Therefore, angle of dip is the angle between earth’s magnetic field and the horizontal direction.
- Horizontal component of Earth's field
At any place earth’s magnetic field (Be) which is working on magnetic meridian can be divided into two components, one is horizontal (BH) and second is vertical (BV).
BE Bv
S BH^ G N In northern hemisphere
(a)
Bv BE
BH
In southern hemisphere
S N (b)
H
Horizontal component of earth’s magnetic field is BH = Be cos Vertical component of earth’s magnetic field is BV = Be sin
B (^) e B (^) H 2 BV^2 ^ ^ tan 1 B B
V H (where^ ^ is the angle of dip)
Important Points :
- At magnetic poles = 90º BH = 0, BV 0
- At magnetic equator = 0º BV = 0, BH 0
- At magnetic equatorial line the magnetic lines of force of earth magnetism are parallel to earth surface i.e., only horizontal component of earth magnetism exists B = BH ( j) i.e., towards south to north.
- Horizontal component of earth magnetic field is from south to north at every point on the earth.
- Vertical component of earth magnetic field is outward (^) ( k^ )in southern hemisphere and inward (^) ( k) in northern hemisphere. Apparent Dip : If a magnetic needle in placed in a plane other the magnetic meridian then the direction indicated by needle in not the direction of resultant magnetic field. In this condition the angle made by magnetic axis of needle with horizontal is called apparent dip.
Bv
BH
Magnetic Meridian
B'H
tan ' BB'^ V (^) BBcoscostan H
V H here = true dip ' = apparent dip = angle of the vertical plane with the magnetic meridian if = 90° then tan' = , ' = 90°
_______________________________________________________________________
Examples ...
Ex.1 Earth’s magnetic field Be at some location is directed at 45° from horizontal. If horizontal component of earth’s magnetic field here is B 0 then earth’s magnetic field Be will be? Sol. BH = Be cos B 0 = Be cos 45° Be = (^) 2Bo Ex.2 At some location, horizontal component of earth’s magnetic field is 3 times of vertical component then inclination of earth’s magnetic field with horizontal will be?
Sol. tan =
B B
B B
v H
v v
3
1 3
30
Ex.3 In the magnetic meridian of a certtain place, the horizontal component of earth's magnetic field is 0.26 G and the dip angle is 60°. Find - (a) Vertical component of earth's magnetic field. (b) The net magnetic field at this place.