Theory of Magnetism, Magnetic Effect of Current For Iit PMT
Theory of Magnetism, Magnetic Effect of Current For Iit PMT
Theory of Magnetism, Magnetic Effect of Current For Iit PMT
XI &XII (CBSE & ICSE BOARD) IIT-JEE / NEET /AIIMS / JIPMER / uptU
MAGNETIC MATERIALS
1. Important definitions and Relations
(i) Magnetising field or Magnetic intensity ( H )
Field in which a material is placed for magnetisation, called as magnetising field.
B0 Magneticfield
Magnetising field = H = = Unit of : Ampere/meter
0 permeabiltyoffreespace
(ii) Intensity of magnetisation ( I )
When a magnetic material is placed in magnetising field then induced dipole moment per unit volume of that material is
M
known as intensity of magnetisation ( I ) I =
V
M IA Ampere meter 2
Unit of I : Ampere/meter [ = = ]
V V meter 3
(iii) Magnetic susceptibility ( m)
I
m = [It is a scalar with no units & dimensions]
H
Physically it represent the ease with which a magnetic material can be magnetised
Note :- A material with more m , can be change into magnet easily.
(iv) Magnetic permeability
Bm TotalMagneticfield inside thematerial
= =
H Magneticfield
It measures the degree to which a magnetic material can be penetrated (or permeated) by the magnetic field line
Bm Wb / m2 Weber HA H
Unit of : = = [ = LI Weber Henry Ampere]
H A/m Am Am m
Relative permeability r = (It has no units and dimensions.)
0
(4) Pole strength (m) : The strength of a magnetic pole to attract magnetic materials towards itself is known as
pole strength.
(i) It is a scalar quantity.
(ii) Pole strength of N and S pole of a magnet is conventionally represented by +m and m respectively.
(iii) It's SI unit is amp m or N/Tesla and dimensions are [LA].
(iv) Pole strength of the magnet depends on the nature of material of magnet and area of cross section. It doesn't
depends upon length.
S N
S N
S
S A more N
N S
SS A less
S N SS
S m more N SS m less
S N
(A) (B)
L w m I
(7) Cutting of a thin bar magnet : For thin magnet b = 0 so L' , w' , m' , I'
n n n n3
(1) Coulombs law in magnetism : The force between two magnetic poles of strength m1 and m2 lying at a
m1m2 0
distance r is given by F k. . In S.I. units k 10 7 wb / Amp m , In CGS units k 1
r 2
4
(ii) Magnetic field due to a bar magnet : At a distance r from the centre of magnet
0 2Mr 0 2M
(a) On axial position : Ba ; If l<<r then Ba
4 (r 2 l 2 ) 2 4 r 3 e
0 M g
(b) On equatorial position : Be ; If l <<r ; Equatorial line
4 (r 2 l 2 )3 / 2
0 M +
then Be N
4 r 3 S
a
2l
(c) General position : In general position for a short bar magnet Axial line
0 M
Bg (3 cos 2 1)
4 r 3
(3) Bar magnet in magnetic field : When a bar magnet is left free in an uniform magnetic field, if align it self
in the directional field.
(i) Torque : = MB sin M B
(ii) Work : W MB(1 cos )
(iii) Potential energy : U MB cos M . B ; ( = Angle made by the dipole with the field)
(4) Gauss's law in magnetism : Net magnetic flux through any closed surface is always zero i.e. B.ds 0
The magnitude and direction of the magnetic field of the earth at a place are completely given by certain.
quantities known as magnetic elements.
(1) Magnetic Declination () : It is the angle between geographic and the magnetic meridian planes.
Declination at a place is expressed at o E or oW
BH N
depending upon whether the north pole of the oW oE
compass needle lies to the east or to the west BV
Geographical B W E
of the geographical axis. meridian
Magnetic
meridian
(2) Angle of inclination or Dip () : S
It is the angle between the direction of intensity of total (A) (B)
magnetic field of earth and a horizontal line in the magnetic meridian.
(3) Horizontal component of earth's magnetic field (BH) : Earth's magnetic field is horizontal only at the
magnetic equator. At any other place, the total intensity can be resolved into horizontal component (BH) and
vertical component (BV). Also BH= B cos ...... (i) and BV B sin ...... (ii)
By squaring and adding equation (i) and (ii) B BH 2 BV 2
BV
Dividing equation (ii) by equation (i) tan
BH
(1) Magnetic maps : Magnetic maps (i.e. Declination, dip and horizontal component) over the earth vary in
magnitude from place to place. It is found that many places have the same value of magnetic elements. The lines are
drawn joining all place on the earth having same value of a magnetic element. These lines form magnetic map.
(i) Isogonic lines: These are the lines on the magnetic map joining the places of equal declination.
(ii) Agonic line: The line which passes through places having zero declination is called agonic line.
(iii) Isoclinic lines : These are the lines joining the points of equal dip or inclination.
(iv) Aclinic line : The line joining places of zero dip is called aclinic line (or magnetic equator)
(v) Isodynamic lines : The lines joining the points or places having the same value of horizontal component of
earth's magnetic field are called isodynamic lines.
(2) Neutral points : A neutral point is a point at which the resultant magnetic field is zero. In general the neutral
point is obtained when horizontal component of earth's field is balanced by the field produced by the magnet.
Tangent Law
mBH
When a small magnet is suspended in two uniform magnetic fields and BH which are
B BH
mB
at right angles to each other, the magnet comes to rest at an angle with respect to BH N
In equilibrium B
S
o
mB
MBH sin MB sin (90 )
B BH tan . This is called tangent law. mBH
Vibration Magnetometer
Vibration magnetometer is used for comparison of magnetic moments and magnetic fields. This device works
on the principle, that whenever a freely suspended magnet in a uniform magnetic field, is disturbed from it's
equilibrium position, it starts vibrating about the mean position.
Torsion head
Time period of oscillation of experimental bar magnet (magnetic moment M)
I
in earth's magnetic field (BH ) is given by the formula. T 2 ;
MBH
wL2
where, I moment of inertia of short bar magnet N S
12
(w = mass of bar magnet)
(1) Determination of magnetic moment of a magnet : The experimental (given) magnet is put into
I 4 2 I
vibration magnetometer and it's time period T is determined. Now T 2 M
MBH B H .T 2
1 (B ) T2
So T 2 H 1 22
BH (BH ) 2 T1
1 M 1 T22
So M
T 2
M 2 T12
Md = M1 + M2
Id I1 I 2
Net moment of inertia Id = I1 + I2 and Td 2 2 ....(ii)
M d BH (M 1 M 2 )B H
1 (M 1 M 2 ) B H
and d . From equation (i) and (ii) we get
2 (I 1 I 2 )
Ts M1 M 2 M 1 Td2 Ts2 s2 d2
Td M1 M 2 M 2 Td2 Ts2 s2 d2
B
(5) To find the ratio of magnetic field : Suppose it is required to find the ratio where B is the field
BH
created by magnet and BH is the horizontal component of earth's magnetic field.
B
To determine a primary (main) magnet is made to first oscillate in earth's magnetic field (BH) alone and it's
BH
I BH
time period of oscillation (T) is noted. T 2
M BH
M BH N S
1
and frequency
2 I
Now a secondary magnet placed near the primary magnet so primary magnet oscillate in a new field with is the
resultant of B and BH and now time period, is noted again.
I
T ' 2
M (B B H )
Pri. Sec.
1 M(B BH )
or ' N S N S
2 I d
2
B '
1
BH
On the basis of mutual interactions or behavior of various materials in an external magnetic field, the materials are
divided in three main categories.
(1) Diamagnetic materials : Diamagnetism is the intrinsic property of every material and it is generated due to
mutual interaction between the applied magnetic field and orbital motion of electrons.
(2) Paramagnetic materials : In these substances the inner orbits of atoms are incomplete. The electron spins
are uncoupled, consequently on applying a magnetic field the magnetic moment generated due to spin motion
align in the direction of magnetic field and induces magnetic moment in its direction due to which the material
gets feebly magnetised. In these materials the electron number is odd.
(A) (B)
When no field is applied (A) Unmagnetised (B) Magnetised
On application of field
(3) Ferromagnetic materials : In some materials, the permanent atomic magnetic moments have strong
tendency to align themselves even without any external field.
These materials are called ferromagnetic materials.
In every unmagnetised ferromagnetic material, the atoms form domains inside the material. Different domains,
however, have different directions of magnetic moment and hence the materials remain unmagnetised. On
applying an external magnetic field, these domains rotate and align in the direction of magnetic field.
(4) Curie Law : The magnetic susceptibility of paramagnetic substances is inversely proportional to its absolute
1 C
temperature i.e. ; where C = Curie constant, T = absolute temperature.
T T
On increasing temperature, the magnetic susceptibility of paramagnetic materials decreases and vice versa.
The magnetic susceptibility of ferromagnetic substances does not change according to Curie law.
(5) Curie temperature (Tc) : The temperature above which a ferromagnetic material behaves like a
paramagnetic material is defined as Curie temperature (Tc). or
The minimum temperature at which a ferromagnetic substance is converted into paramagnetic substance is
defined as Curie temperature. For various ferromagnetic materials its values are different, e.g. for Ni, TCNi 358 o C
for Fe, TCFe 770o C for CO, TCCO 1120 o C
At this temperature the ferromagnetism of the substances suddenly vanishes.
(6) Curie-weiss law : At temperatures above Curie temperature the magnetic susceptibility of ferromagnetic
materials is inversely proportional to (T Tc)
1 C
i.e.
T Tc (T Tc )
(1) Retentivity : When H is reduced, I reduces but is not zero when H = 0. The F
E
remainder value OC of magnetization when H = 0 is called the residual
magnetism or retentivity.
The property by virtue of which the magnetism (I) remains in a material even on the removal of
magnetizing field is called Retentivity or Residual magnetism.
(2) Coercivity or coercive force : When magnetic field H is reversed, the magnetization decreases and for a
particular value of H, denoted by Hc, it becomes zero i.e., Hc = OD when I = 0.
This value of H is called the coercivity.
Magnetic hard substance (steel) High coercivity
Magnetic soft substance (soft iron) Low coercivity
(3) When field H is further increased in reverse direction, the intensity of magnetization attains saturation value in
reverse direction (i.e. point E)
(4) When H is decreased to zero and changed direction in steps, we get the part EFGB.
Thus complete cycle of magnetization and demagnetization is represented by BCDEFGB. This curve is known as
hysteresis curve
Comparison between soft iron and steel
Soft iron Steel
I I
H
H
The area of hysteresis loop is less (low energy loss) The area of hysteresis loop is large (high energy
loss)
Less relativity and coercive force More retentivity and coercive force
Used in dynamo, transformer, electromagnet tape Used for making permanent magnet.
recorder and tapes etc.
Explanation of magnetism On the basis of orbital motion of On the basis of spin and orbital On the basis of domains formed
electrons motion of electrons
Behaviour In a non-uniform magnetic These are repelled in an external These are feebly attracted in an These are strongly attracted in an
field magnetic field i.e. have a tendency external magnetic field i.e., have a external magnetic field i.e. they
to move from high to low field tendency to move from low to high easily move from low to high field
region. field region region
Pushed up Very strong
Pulled in
pull
N S N S
N S
State of magnetisation These are weekly magnetised in a These get weekly magnetised in These get strongly magnetised in
direction opposite to that of the direction of applied magnetic the direction of applied magnetic
applied magnetic field field field
When the material in the form of Liquid level in that limb gets Liquid level in that limb rises up Liquid level in that limb rises up
liquid is filled in the U-tube and depressed very much
placed between pole pieces.
N S N S N S
On placing the gaseous materials The gas expands at right angles to The gas expands in the direction of The gas rapidly expands in the
between pole pieces the magnetic field. magnetic field. direction of magnetic field
The value of magnetic induction B B < B0 (where B0 is the magnetic B > B0 B >> B0
induction in vacuum)
Magnetic susceptibility Low and negative || 1 Low but positive 1 Positive and high 102
Dependence of on temperature Does not depend on temperature On cooling, these get converted to These get converted into
(except Bi at low temperature) ferromagnetic materials at Curie paramagnetic materials at Curie
temperature temperature
T T TC T
Intensity of magnetisation (I) I is in a direction opposite to that of H I is in the direction of H but value I is in the direction of H and
and its value is very low is low value is very high.
I-H curves
+I Is
H
I H
Hs H
Magnetic moment (M) Very low ( 0) Very low Very high
Examples Cu, Ag, Au, Zn, Bi, Sb, NaCl, H2O Al, Mn, Pt, Na, CuCl2, O2 and Fe, Co, Ni, Cd, Fe3O4 etc.
air and diamond etc. crown glass
Magnetic moment of straight current carrying wire is zero. Remember time period of oscillation in difference
position is greater than that in sum position Td > Ts .
Magnetic moment of toroid is zero
Atoms which have paired electron have the magnetic If a rectangular bar magnet is cut in n equal parts
1
moment zero. then time period of each part will be times that of
n
Magnetostriction : The length of an iron bar changes T
complete magnet (i.e. T ' ) while for short magnet
when it is magnetised, when an iron bar magnetised it's length n
increases due to alignment of spins parallel to the field. This
T
increase is in the direction of magnetisation. This effect is T' . If nothing is said then bar magnet is treated as
n
known as magnetostriction. short magnet.
When a magnetic dipole of moment M moves from Suppose a magnetic needle is vibrating in earths magnetic
unstable equilibrium to stable equilibrium position in a field. With temperature rise M decreases hence time period (T)
magnetic field B, the kinetic energy will decrease by 2 increases but at 770oC (Curie temperature) it stops vibrating.
MB.
An iron cored coil and a bulb are connected in series with
Intensity of magnetisation (I) is produced in materials due
an ac generator. If an iron rod is introduced inside a coil,
to spin motion of electrons.
then the intensity of bulb will decrease, because some
For protecting a sensitive equipment from the external energy lost in magnetising the rod.
magnetic field it should be placed inside an iron cane. (magnetic
shielding)
Hysteresis energy loss = Area bound by the
hysteresis loop = VAnt Joule;
B=0 Where , V = Volume of ferromagnetic sample,
A = Area of B H loop P,
BV BV
' apparent angle of dip and tan '
BH' BH cos
tan
tan ' Magnetic meridian
cos BH
BH cos
B
BV
Inclined plane