Magnetism (1)full notes revision handy.ppsx

Magnetism

1. MAGNETISM & MATTER

2. Introduction
•The earth is a magnet pointing from the geographic south to the north
•When a bar magnet is suspended freely it comes to rest and points in
the north south direction. The tip pointing to the geographic north is
called the north pole and the tip pointing to the geographic south is
the south pole.
•N-N and S-S repel each other, N-S poles attract each other
•North and south poles of a magnet can never be isolated. Magnetic
monopoles do not exist.
•It is always possible to make magnets out of iron and its alloys.

3. The Bar Magnet
Properties of Bar Magnets
•They form a continuous closed loops unlike electric
dipoles which start at a positive charge and end at the
negative charge
•The tangent to the field line at a given point represent
the net magnetic field at the point
•Greater the number of lines per unit area stronger
is the magnetic field
•Magnetic field lines never intersect.

4. Terms Related to the Bar Magnet
•Magnetic poles – Regions of concentrated magnetic strength.
•Magnetic axis – The line passing through the poles of the magnet is
called the magnetic axis of the magnet.
•Magnetic equator – the line passing through the centre of the
magnet and perpendicular to the magnetic axis.
•Magnetic length - the distance between the poles of the magnet is
called the magnetic length. It is slightly less than the geometric
length.

5. Coulombs Law of Magnetic Forces, Magnetic
Dipole Moment
F =
K =
q
m1
, q
m2
= pole strengths of the two magnetic poles
r = distance between the two poles
= x 2

6. Magnetic field- Axial Point (Bar Magnet)
F
N = along NP
F
S
= along PS
B
axial
= F
N
– F
S
= -
= - = () = ()
For a short bar magnet l<<<r B
axial = ()

7. Magnetic field - Equitorial Point (Bar Magnet)
NS
O
r
P
Q
T
R
⃗??????
??????
⃗
??????
??????
⃗??????
θ
θ
θ
θ
l l
x
x

=

F
N
= along NP
F
S = along PS
B
equi
= F
N
cosθ + F
S
cosθ = 2F
N
cosθ
= =
For a short magnet
B
equi
= ()

8. Bar Magnet & Solenoid - Similarities
2l = length of the solenoid
n = number of turns per unit length
a = radius of the solenoid
Magnetic field due to circular loop
=
For a small element dx the number of turns will be ndx
Hence =
=
= =
If r >> x then (r-x) ≈ r
Then (r-x)
2
+ a
2
≈ r
2
+ a
2
≈ r
2
( since r
2
>> a
2
)
= =
2l = -------- (1)
m = NIA = n (2l) Iπa
2
m/2π = nlIa
2
--------------- (2)
Substituting (2) in (1) we get
= =

9. Magnetic Dipole in Uniform Magnetic Field
Comparing with
= - ω
2
x
ω
2
=
ω =
Thus (
2
= or T = 2π
Deflecting Torque = x = mBsinθ,
Restoring torque = Iα
Iα = - mBsinθ
Iα = I = I = - mBsinθ
For small angles sinθ = θ
Thus I = - mBθ
= - θ ---------------- (1)

10. Potential Energy of Magnetic Dipole
τ = = mBsinθ
dW = τ dθ
W = U
f
–U
i
= = d
U = mB [-cosθ ] = mB (cosθ
i
– cosθ
f
)
U
min
= mB (cos180 – cos0) = -2mB
U
max
= mB (cos0 – cos180) = 2mB

11. Problems
A current of 7A is flowing in a plane circular coil of radius 1cm and having 100 turns.
The coil is placed in a uniform magnetic field of 0.2 Wb/m
2
. If the coil is free to rotate
what would correspond to the (i) the most stable equilibrium and (ii) most unstable
equilibrium? Calculate the potential energy of the coil in each case.

12. Electrostatics & Magnetism
  ElectrostaticsMagnetism
Dipole moment
Equitorial point
Axial Point
Torque x x

13. Gauss’s Law of Magnetism
= 0
S

14. Earths Magnetic Field
•Geographic axis : The straight line passing through the geographical north and south
poles of the earth is the geographic axis. It is the axis of rotation of the earth.
•Magnetic axis: The straight line passing through the magnetic north and south poles
of the earth is called its magnetic axis. The magnetic axis makes an angle of 11.3
o
with
the geographic axis currently.
•Magnetic equator: It is the great circle on the earth perpendicular to the magnetic
axis.
•Magnetic meridian : the vertical plane passing through the magnetic axis of a freely
suspended small magnet is called the magnetic meridian. The earths magnetic field
acts in the direction of the magnetic meridian.
•Geographic Meridian : The vertical plane passing through the geographic north and
south poles is called the geographic meridian.

15. Elements of the Earths Magnetic Field
Earths Magnetic field can be described by three components
•Magnetic Declination
•Angle of dip
•Horizontal component of the earths magnetic field

16. Magnetic Declination
The angle between the geographic meridian
and the magnetic meridian is called the angle
of declination(α) of that place.
α

17. Angle of Dip
The angle made by the earths total magnetic
field with the horizontal direction in the magnetic
meridian is called the angle of dip (δ) at any place

18. Horizontal Component of the Earths Magnetic
Field
B
H
= Bcosδ and B
V
= Bsinδ
B
V
/ B
H
= Bsinδ/ Bcosδ
B
V/ B
H = tanδ
Also B =

19. Problems
If the horizontal component of the earths magnetic field at a place where the angle of
dip is 60
o
is 0.4 x 10
-4
T calculate the vertical component and the resultant magnetic
field at that place.

20. Neutral Points
At the neutral points
B
H
= () for a short bar magnet.
Or B
H
=

21. Neutral Points
At the neutral points
B
H
= () for a short bar magnet.
Or B
H
=

22. Problems
A bar magnet of length 10cm is placed in the magnetic meridian with the north pole
pointing towards to geographic north. A neutral point is obtained at a point 12cm from
the centre of the magnet. Find the magnetic moment of the magnet if B
H
= 0.34G

23. Terminology – Magnetic Materials
(Properties)
•Magnetising field : The magnetic field that induces magnetism in a
material is called magnetizing field .
B
0
= µ
o
nI is the magnetizing field
•Magnetic induction : Surface current I
M induces magnetic field B
M
inside the material
B
M = µ
onI
M
• Total magnetic field inside the material (Magnetic Induction)
B = B
o + B
M
•SI unit of magnetic induction is tesla (T) or Wb/m
2
or N/mA or J/Am
2
.

24. Terminology – Magnetic Materials
(Properties)
•Magnetising field intensity : Ability of magnetising field to magnetize a material (H).
Number of ampere turns (nI) flowing around a unit length of a solenoid
H = nI
B
0 = µ
onI = µ
oH or H = B
0/µ
o
[L
-1
A] and its SI unit is A/m
•Intensity of Magnetisation: magnetic moment developed per unit volume of the
material is called as intensity of magnetization (Magnetisation)
M = m/V.
M = nI
M
A/A = nI
M

B
M = µ
onI
M , B
M = µ
oM
B = B
o
+ B
M
= µ
o
H + µ
o
M = µ
o
(H + M)

25. Terminology – Magnetic Materials
(Properties)
•Magnetic Permeability : The ratio of the magnetic induction to the magnetic intensity
µ = B/H
Unit of µ is Tm/A. Dimensions are [MLT
-2
A
-2
]
•Relative permeability : Ratio of the permeability of the medium to the permeability of free space
µ
r = µ/µ
o
•Magnetic susceptibility : Ratio of intensity of magnetization M to the magnetizing field intensity H.
χ
M = M/H .
B = µ
o
(H + M)
But B = µH
Thus µH = µ
o(H + M)
µH = µ
oH(1 + M/H) = µ
oH(1 + χ
M )
µ = µ
o
(1 + χ
M
) = µ
r
µ
o
µ
r
= (1 + χ
M
)

26. Problems
A solenoid having 500 turns/m is carrying a current of 3A. Its core is made of iron
which has a relative permeability of 5000. Determine the magnitudes of the magnetic
intensity, magnetisation and magnetic field inside the core.

27. Classification of Magnetic Materials
•Diamagnetic Materials
•Paramagnetic Materials
•Ferromagnetic Materials

28. Diamagnetic Materials
Bi, Cu, Pb :Magnetic moments of electrons cancel out each other
In a magnetic field the speed of the electrons whose
magnetic moment is in the direction of the external
magnetic field decreases and in the opposite direction
increases.
χ
M
is small and negative.
µ
r = (1 + χ
M ) is positive but less than 1.

29. Paramagnetic Materials
Molecules possess permanent magnetic moment due to
presence of unpaired electrons
Field tends to align the magnetic moments in its direction
producing a weak magnetic moment along B
Intensity of magnetization
Directly proportional to the magnetizing field intensity H
Inversely proportional to the temperature
M α H/T
M = C (H/T) or M/H = C/T
χ
M
= C/T

χ
M
is positive µ
r
slightly > 1.

30. Ferromagnetic Materials
Ferromagnetism - explained on the basis of domain theory
Individual atoms have large magnetic moments.
On heating the change in the magnetic properties of the
material is very abrupt
Transition occurs at Curie temperature
B
χ
M = C/(T-T
C)
χ
M µ
r are positive and very high (order of hundreds)

31. Hysteresis Loop
OC – Retentivity or Remenance
OD - Coercivity
Electromagnets & Transformers - low retentivity,
coercivity and narrow hysteresis loop
Area of the hysteresis loop represents the energy
dissipated per unit volume in the material
Permanent magnets - high retentivity, coercivity
and wide hysteresis loop

32. THE END