Magnetic Fields
S. Nirmalan
A region in which magnetic force acts is called a magnetic field. They are
invisible and found around magnets, planets and wires carrying current.
Magnetic fields exert a force on
1. magnetic material (Nickel, Cobalt, iron ,steel)
2. other magnets
3. a wire carrying an electric current provided field and current are not
parallel
4. Moving charges if they are not parallel to the field
Magnetic field patterns
1. Bar magnet
2. Horseshoe magnet
3. Cylindrical magnet
4.magnadur magnet
The direction of a magnetic field at any point is taken to be the direction of the
magnetic force which would act on a free N pole placed at that point.
The direction of the magnetic field is the direction in which the N pole end of a
plotting compass needle would point.
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x - Neutral point
A neutral point is a Position within overlapping magnetic fields where the fields
cancel so that the resultant magnetic field is zero.
Q.A solenoid is 35cm long and has 100 turns. Diameter is 9cm. the solenoid is
placed in a redial magnetic field of strength 200mT. Calculate the magnetic force
on the solenoid when a current of 4.2A flows.
The Force on a current carrying conductor in a magnetic field
A current carrying conductor in a magnetic
field experiences a force provided the conductor
is not parallel to the field. The force has its
maximum value when the conductor is
perpendicular to the field.The force depends on,
1. The strength of the magnetic field (B)
2. The size of the currents (B)
3. The length of the conductor within the
magnetic field (l)
An increase in any of these three produces an increase in the magnitude of the
force acting.
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F B
&
F I
&
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F 
F  BI 
F  BI
F  B I  sin 
If    0
If the conductor is at an angle;
F 0
C
  90 F  B I 
B
A

The direction of the force can be found using Fleming’s Left Hand Rule.
Flemings Left Hand Rule
If the first and second fingers and the thumb of the
left hand are placed at right angles to each other, with
the first finger pointing in the direction of the field
and the second finger pointing in the direction of the
current , then the thumb points in the direction of the
force.
Magnetic Flux Density / Magnetic Field Strength (B)
The force on one meter length of a straight wire carrying a steady current
of 1 A when placed perpendicular to a magnetic field unit - Tesla
Definition of Tesla
The magnetic flux density that produces a force of 1N on each meter length of
wire carrying a current of 1A perpendicular to the magnetic field.
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Magnetic Flux ()
Total amount of magnetism through an area and it is defined as;
 = BA
Magnetic flux = magnetic flux density x area
(Tm2 = Wb) Unit = Webber
Magnetic Flux Linkage
When a coil having N turns surrounds a magnetic flux , each turn links the flux
. So the total magnetic flux linking the coil is the product of magnetic flux and
number of turns.
Magnetic flux linkage = magnetic flux x number of turns
= N = NBA
Q.The diagrams show three situation involving a wire carrying a current
through a magnetic field .for each situation find the direction of the stated
quantity.
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Magnetic Force on a moving charged particle
A charged paraticle moving in a magnetic field experiences a force provided the
field is not parallel to the particle. The force has its maximum value when the
particle moves perpendicular to the field.
F  B q v sin 
If the particle moves at right angles to the magnetic field the force is given by
F  Bqv
The direction of the force is perpendicular to their direction of motion. This
causes charged particle to perform circular motion. Speed of charge particle
remains constant.the magnetic field provides the centripetal force needed for
this circular motion.
mv
Bqv 
r
2

r 
mv
Bq
r 
p
Bq
D.C electric motor
A simple motor to work from direct
current consists of a rectangular coil of wire mounted
on an axle which can rotate between the poles of a Cshaped magnet. Each end of the coil is connected to
half of a split ring of copper, called a commutator,
which rotates with the coil. Two carbon blocks, the
brushes,, are pressed lightly against the commutator
by springs. The brushes are connected to an electrical
supply. if Fleming’s left hand rule is applied to the coil
in the position shown, we find that side ab
experiences an upward force and side cd a downward
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force. These two forces form a couple which rotates
the coil.
Moving coil loud speaker
The cylindrical magnet produces a strong
radial magnetic field at right angles to the wire in
the coil. The coil is free to move backwards and
forwards and is attached to a stiff paper or
plastic cone. The loud speaker is connected to an
amplifier which gives out alternating current
.since the alternating current through the wire
changes direction it experiences a backward and
forward force .as a result; the cone vibrates and
gives out sound waves.
Electromagnetic induction
Production of electricity by the relative motion between magnetic fields and
conductors. This is the principal of generators and transformers.
When a conductor cuts the magnetic fields an e.m.f
/voltage is induced. Induced
voltage depend on
Magnetic field strength (B)
Speed of motion of the magnet
or coil (v)
Length of wire (l)
Number of turns in the coil (N)
E. M . Finduced  B l v N
E 
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N 
t
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Faradays Law
E 
N   The magnitude of an induced e.m.f is directly proportional to the
t
rate of change of magnetic flux linkage .
Lenz’s Law
The Direction of the induced current is such as to oppose the change causing it.
North pole of the magnet approaches the
coil.according to lenz’s law the induced current should
flow in a direction that makes the coil behave like a
magnet with its top a north pole. The downward
motion of the magnet will then be opposed since like
poles repel.
When the magnet is withdrawn, the top of
the coil should become a south pole,and attract the
north pole of the magnet ,so hindering its removal.
When magnet and coil are stationary, there is no deflection on the galvanometer.
There is no relative emotion. So the rate of change of magnetic flux linkage is
zero.( e.m.f is zero).The direction of the induced current can be found using
Fleming’s right hand rule.
Fleming’s right hand rule
If the first and second fingers and the thumb of the
right hand are placed at right angles to each other,
with the first finger pointing in the direction of the
field and the thumb pointing in the direction of the
motion of the wire , then the second finger points in
the direction of the induced current.
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Bar magnet falling through the coil
If a bar magnet is dropped through a coil, the flux through the coil increases as
the bar magnet enters and decreases as it leaves. An e.m.f is induced across the
coil as magnetic flux through it changes. the magnet is accelerating under
gravity. it leaves the coil slightly faster than it enters. The maximum induced
e.m.f is greater as the magnet exists ,although this e.m.f is induced for a shorter
time.
Transformers
An alternating voltage applied to the primary produces an alternating current
through the primary coil. a changing magnetic field is produced which cuts the
secondary coil since the soft iron core traps most of the magnetic field .there is
now a rate of change of magnetic flux linkage in the secondary coil and an
alternating voltage is induced in the secondary coil due to electromagnetic
induction ..
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VS
NS

VP N P
Vp - primary voltage
Vs - secondary voltage
Np - number of turns on secondary coil
Ip – primary current
Ns - number of turns on secondary coil
Is - secondary current
If Ns > Np, then Vs > Vp , this type of transformer is called a step up transformer.
If Ns < Np, then Vs < Vp , this type of transformer is called a step down
transformer.
If the transformer is 100 % efficient, its an ideal transformer.
So the Power output = Power input
Vp Ip = Vs I s
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The structure of an Atom
Matter is made up of smaller particles called atoms. The three principal parts of
the atom are the proton, neutron and electron. Protons and neutrons are bound
together in the nucleus. Electrons orbit the nucleus.
10-10m
.
Diameter of an atom =10-10m
atom
nucleus
Diameter of a nucleus =10-15m
10-15m
The Protons and neutrons are called nucleons.
Particle
Mass
Charge
Proton
1u  1.67  10 27 kg
1.6  10 19 C
Neutron
1u  1.67  10 27 kg
0
Electron
Symbol
1
P
1
1
1u
 9.1110 31 kg
1840
n
0
0
-11 .6  10 19 C
1u = atomic mass unit
e
Normally atom is neutral. This means that it has equal number of positive
(protons) and negative (electrons) charges.
Proton Number or Atomic Number (Z)
The total number of protons in the nucleus of an atom. (If atom is neutral proton
number is equal to the number of electron)
Neutron Number (N)
A=Z+N
The total number of neutron in the nucleus.
Mass Number or Nucleon Number (A)
The total number of protons and neutrons in an atom is called its mass number.
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If an element
with a chemical symbol X has a mass number A an atomic number
A
X
Z
proton
Z, its nucleus
is represented by the
symbol.
4
For Example: 23
11
2
Protons
Neutrons
Protons
He nucleus
Neutrons
Na atom
Electrons
Electrons
At different times, scientists have proposed various descriptions or models of
the atom. following Thomson’s discovery of the electron in 1897, one of the first
atomic models proposed was the “plum pudding” model. In this model atom was
assumed to be a sphere of uniform positive charge with negatively charged
electron spread through it. (it is like plums in a pudding) In 1911 Geiger and
Marsden performed Alpha particle scattering experiment under the direction of
(Ernest) Ruther ford, which led to a new model of the atom.
Alpha particle scattering Experiment
Lead
Vacuum
tube
Screen
4
(Coated with Zinc sulphide)
2
Alpha source
(Radium
source in
lead box)
Thin gold foil

4
He
2
197
Au
79
.
.
.
.
.
.
.
. .
.
.
. .
.
. .
1) A thin gold foil was bombarded with alpha particles.
2) Alpha particles leaving the foil were detected by observing flashes of light
(which they caused on a glass screen coated with zinc sulphide.
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Angle of
Evidence
deflection/degrees
Most alpha particles pass
0 – 10
straight through with little
deviation.
Conclusion
Most of the atom is
empty space.
All the atom's positive
10 – 90
90 – 100
Some alpha particles deflected
charge is concentrated in
through a large angle.
one place.
A few alpha particles are
Most of the mass, and all
repelled back towards the
positive charge, is in a
source side of the foil.
tiny, central nucleus.
Target - Gold atom or (Gold foil)
Incident particle = Alpha particles
Electron beams
Free conduction electrons in metals need a certain amount of energy if they are
to escape from the surface of the metal structure. This energy can be supplied by
a beam of photons, as seen in the photoelectric effect. The electrons can also
gain enough energy simply through heating of the metal.
The release of
electrons from the surface of a metal as it is heated is known as thermionic
emission.
Electron diffraction
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The Low voltage power supply heats up the cathode and so gives the atoms
enough energy for them to emit electrons. This is called thermionic emission.
The EHT power supply attracts electrons from the filament to positive plate
which has a piece of graphite fixed in the middle .The fluorescent screen gives
out light whenever it is hit by electrons.
The layer of atoms in graphite produce electron superposition patterns.
Pattern is a regular circular ring
Electrical Potential Energ lost  Kinetic Energy gained
vQ 
1
m v2
2
De Broglie’s Theorem
Electrons, like other particles, have wave properties, with wave length that is
dependent on the momentum of the particle. His equation states that
1P  h P
  h mv
where,   De Broglies wave length
h  Planckscons tan t
The wave length of electron is nearly equal to the atomic spacing. Diffraction
takes place when electrons pass through the graphite. This result supports more
that electrons behave like waves
Q1.How fast would an electron be moving if it was accelerated from rest through
a pd of 2500 V?
Q2.What is the wavelength of an electron in a beam which has been accelerated
through 2000 V?
Q3Calculate the de Broglie wavelengths for the following:
a. an electron travelling at 2 % of the speed of light
b. an electron which has been accelerated through 1200 V
c. a proton with a momentum of 5 x 10-21 kgms-1
d. you running at 5 ms-1
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Particle accelerators
The only way to find how matter is constructed(internal substructure of
particles), is to break it apart with fast-moving particles produced by an
accelerator.it is necessary to use high energy particles because at lower energies
particles just bounce off each other ,keeping their internal secret.charged
particles can be accelerated in straight lines using a potential difference,and
their direction changed along a curved path by a magnetic field.
The linac (Linear Accelerators)
1. This Consists of metal cylindrical tubes in an evacuated tube.
2. High frequency high voltage potential difference is applied to the tubes
3. The Polarityof the potential difference applied to each tube changes as the
particle leaves the previous tube.
4. Particles travel at a constant speed within each tube and are accelerated
between the tubes
5. Each tube is longer than the previous one because the accelerated particles
are traveling increasing distances in the time taken for half of one complete
cycle of the applied voltage to occur.
Q1A particular linac has 420 metal tubes and the peak voltage of the alternating
supply is 800kv.show that the emerging protons have gained a kinetic energy of
about 5x10-11J and express the mass equivalent of this energy as a fraction of the
mass of a stationary proton. Take the mass of a proton as 1.01u.
The Frequency of the alternating supply is 390 MHz. Calculate how long it takes
a proton to travel along the linac.
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The Cyclotron
Bqv 
T 
mv2
r

2 r
2

v
v
T 
f 
f 
x
mv
Bq
r

mv
Bq
2 m
Bq
2 m
Bq
1 2 m
1

r
Bq
Bq
2 m
This Consists of two semicircular boxes (called dees)separated by a small gap
and contained in an evacuated chamber
A uniform magnetic field provided by large electromagnet is applied
perpendicular to the dees.
A high frequency high voltage alternating potential difference is connected
between the dees
Changed particles produced by an iron source at the centre of the device and
move along a circular path.
Particles are accelerated every time it crosses from one dee to the other and they
move at a constant speed in a circular path within each dee.
Polarity of the p.d applied to each dee changes as the particle is just about to
leave the dee
The problem with the cyclotron is that it loses synchronization at high speed.
Because the mass of the particle increases with speed. This gives an upper limit
to the energy of the particle.
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The synchrotron
This has a fixed radius
As the particles are accelerated the strength of the
magnetic field is increased and the frequency of the a.c
supply is synchronized to take account of the increasing mess of the
particles as they approach the speed of light
Cloud chamber
The cloud chamber consists of glass vessel
containing super saturated alcohol vapour(As
much vapour as possible dissolved in the air but
with no condensation present).
If any charge particle moves through the vessel it will ionize air molecules along
its path.
Alcohol starts to condense along its path forming alcohol droplets. The result is
a vapor trail which indicates the path of the particle.
Bubble chamber
1. The bubble chamber consists of superheated liquid hydrogen under
pressure.(liquid is held at a temperature above its boiling point,but under
pressure so that it does not boil)
2. Charged particles passing through it ionises the liquid hydrogen.
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3. When the pressure is released and the liquid starts to boil first in the region
where there are ions, producing bubbles
4. The bubbles are allowed to grow for a time and then the whole chamber is
photographed.
Spark detector
A sealed glass tube filled with inert gas
consists of wires or plates carrying high
potential.
charge particles moving through gas
ionises air molecules
these ions/electrons accelerate towards wires causing more
ionization.
This leads to a spark
Every time a spark is produced a tiny current flows in the wires
nearest to it.
A computer can quickly reconstruct the paths of the particles using
the electrical signal.
The spark chamber
the wire spark chamber
Analyzing particle tracks
Track length :- This is related to the particle energy. Particle which has
greater energy produces longer track.
Track thickness :- This is related to charge of particle (ionizing ability) which
depends of charge and speed.
Curvature of track :- The sign of the charge particle can be found from the
direction of deflection.
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Deflection :- Apply magnetic field perpendicular to its path. When particle
speed decreases (as it loses energy due to ionization) it spirals inwards and
the track also becomes thicker.
Missing tracks :- shows the presence of neutral particles
Advantages of spark chamber
Can record many times per second
Electrical signal can be fed to computer (it is no longer necessary to
photograph).
Speed of the particles can be deduced
Electronvolt (eV)
The energy gained by an electron traveling through a potential difference of 1
volt. 1eV=
Unified Atomic Mass Unit (u)
One atomic mass unit is defined as one – twelfth of the mass of one atom of the
C-12 atom. 1u = 1.66 x 10-27kg
Einstein’s mass – energy relation
According to the Einstein’s special theory of relativity a mass m is equivalent to
an amount of energy E, where
E  m c2
C - Speed of light
Antimatter or Antiparticle
Matter with equal mass but opposite charge and spin to ordinary matter, for
example the positron is the anti particle to the electron. It is difficult to store
antimatter. As soon as it touches the matters/container, matter and anti matter
annihilate.
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Photon - photon is a tiny energy packet of e m radiation.E=hf
Annihilation – (Reaction) of particles
A reaction between a particle and its antiparticle in which the particles turn into
electromagnetic radiation. The mass of the energy released is equal to the mass
electron + positron  photon
of the two particles annihilate
Electron-positron Pair production
The creation of an electron -positron pair from a gamma ray photo.
photon  electron + positron
Q1.A gamma ray photon converts into an electron and a positron (an antielectron which has an identical mass to the electron).calculate the frequency of
the gamma photon
Q2Show that the minimum -ray energy necessary of electron - positron
production is 1.02 MeV.
Deep Inelastic Scattering
Low energy electron
Proton
Low energy
electron
High energy
electron
Proton
or neutron
X
x
X
quarks
Inciden t particle = high energy electron
Target – Proton or neutron
High energy electrons are fired at the protons to probe the distribution of charge
within the proton. High energy electron penetrating the nucleus collides with the
quarks in it and are scattered during the collision electron loses energy. So it is
an inelastic collision.
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Fundamental particles (A particle which cannot be further divided)
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A fundamental particle is one which cannot be split into anything smaller. It has
no internal structure or components. There are twelve fundamental particles.Six
Quarks and six leptons.
Quarks
The fundamental particles from which protons, neutrons (and some other
particles) are made. Quarks can interact via the strong nuclear force. . Quarks
never occur alone. There are six types of quarks.
Strong nuclear force - the force which binds nucleons together in the nucleus.
The family of quarks. These are subject to the strong nuclear force.
Leptons
Fundamental particles (they have never been split apart into smaller
components) with a very small mass. There are six types of leptons. They are
like point no radius.
The family of leptons. These do not feel the strong nuclear force.
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Hadrons - Groups of quarks held together by strong forces baryons and mesons
Hadron is a heavy particle made from quarks. Quarks never occur alone. They
always occur in combination of two or three, forming the hadrons. There are
three types of hadrons.Mesons,Baryons,Anti baryons
Mesons
If a quark and an anti-quark are combined together, the resulting particle is
known as a meson . The pion and the kaon are the most common example of
mesons.
Baryons
If three quarks are combined together, the resulting particle is a baryon. Protons
and neutrons are baryons.
Reactions conserve properties
In order for any particle reaction occur, the overall reaction must conserve
various properties of the particles involved.
iCharge
iii. Mass/energy
ii.Momentum
particle
v.lepton number(L)
iv.baryon number(B)
baryon number
quark
anti quark
baryon
anti baryon
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vi.strangeness (S)
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meson
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