This document provides an overview of electrical and magnetic force fields. It discusses: 1) The electrical force and how it is balanced by quantum mechanics in atoms. 2) Electric and magnetic fields, which are vector fields associated with every point in space. 3) Key characteristics of vector fields including flux and circulation. 4) The laws of electromagnetism, including how electric and magnetic fields interact. 5) Different types of magnetism exhibited by materials, including diamagnetism, paramagnetism, and ferromagnetism in iron. Quantum mechanics is needed to fully understand magnetic effects.

1. ELECTRICAL & MAGNETIC FORCE FIELDS
Training Lecture series
PORTESCAP
Dr. N. M. Singh
Centre of Excellence, Complex and Nonlinear Dynamical Systems
VJTI, Mumbai

2. ELECTRICAL & MAGNETIC FORCE FIELDS
1. The Electrical Force
2. Electric & Magnetic Fields
3. Characteristics of Vector Fields
4. Laws of Electromagnetism
5. Diamagnetism and Paramagnetism

3. • Billion-Billion times stronger.
• Two kinds of matter “Positive”
& “ Negative.
• Attract and Repel both
operates.
• An evenly mixed bunch of
positives and negatives would
do something completely
different. What??
• Billion-Billion times weaker.
• In Gravity there is only attraction.
• No concept of positive-negative.
• Why is so much disparity between
these two kinds of forces??
Tricked the Scientific community
even Einstein.
1. Electrical Force

4. 1% more
electrons or
protons

5. "If this electrical force is so terrific, why don't the protons and electrons
just get on top of each other?
The Uncertainty Principle & Laws of Quantum Mechanics keep a limit
on the attraction of opposite charges
In an atom , "What holds the nucleus together"? There are several
protons, all of which are positive. Why don't they push themselves apart?

7. • Nuclear forces, which are greater than the electrical forces and
which are able to hold the protons together in spite of the electrical
repulsion.
• The nuclear forces, however, have a short range.
• If a nucleus has too many protons , it gets too big, and it will not
stay together. An example is uranium, with 92 protons.

8. • In uranium, the balance between nuclear &
electrical force is so delicate that the nucleus is
almost ready to fly apart.
• As such an equilibrium gets disturbed, the
energy released in the process is usually called
"nuclear" energy, but it is really "electrical"
energy released when electrical forces have
overcome the attractive nuclear forces.
• The electrical force, like a gravitational force, decreases inversely as
the square of the distance between charges (Coulomb's law).
• The electrical forces depend also on the motions of the charges in a
complicated way.
Why Electromagnetism?

9. • Caused by the motion of charges or moving
charges, we call it the magnetic force.
• It is really one aspect of an electrical effect. That is
why we call the subject electromagnetism.
• force that acts on a particular charge,
• If Force is known, motion of a particle is given by,
• Both Electric & Magnetic Fields follow the
Principle of Superposition.
𝐹 = 𝑞(𝐸 + 𝑣 × 𝐵
E the electric field and B the magnetic field at the
location of the charge.
2
2
( )
1
d mv
F q E v B
dt v
c
   


10. 2. Electric & Magnetic Fields
• Associate with every point (x, y, z) in space two vectors E and B,
which may be changing with time.
• The electric and magnetic fields are, then, viewed as vector functions
of x, y, z, and t.
• Since a vector is specified by its components, each of the fields E (x,
y, z, t) and B (x, y, z, t) represent three mathematical functions of x,
y, z, and t.
A vector field:
drawing a set
of arrows with
magnitudes and
directions
A vector field:
drawing lines tangent
to the direction of the
field vector at each
point, and by drawing
the density of lines
proportional to the
magnitude of the field
vector.

11. • E (or B) can be specified precisely at every point in space, hence, is
called a "field“.
• Simply consider the fields as mathematical functions of position and
time.
time-dependent temperature field "velocity field" of a flowing liquid.
 
, , ,
T x y z t  
, , ,
v x y z t
Ordinary Electrical charges produce field lines
Spreading to infinity in the empty space.
EM Field of a human heart

12. 3. Characteristics of Vector Fields
Flux = (average normal component)·(surface area)
Does the field have a quality of "outflow"?

13. • Second property of a vector field that has to do with a line.
• Think of a velocity field that describes the flow of a liquid. We might
ask this interesting question: Is the liquid circulating?
Is there a net rotational motion around some loop?
Circulation = (average tangential component).(distance around)
The velocity fleld in a
liquid.
Consider an arbitrary
uniform cross-section tube
If the liquid were suddenly
frozen everywhere except
inside the tube, the liquid
in the tube would circulate

14. 4. The Laws of Electromagnetism
• The first law of electromagnetism describes the flux of the electric field:
• Measure the circulation of the electric field around an arbitrary curve in
space. For electricity there is a second law that states:
for any surface S (not closed) whose edge is the curve C,
• We can complete the laws of the electromagnetic field by writing two
corresponding equations for the magnetic field B.
0
the net charge inside
The flux of E through any closed surface =

Circulation of E around C = (flux of B through S)
d
dt

15. Flux of B through any closed surface = 0
• For a surface S bounded by the curve C,
• Magnetism is in reality a relativistic effect of electricity.
• Some of the laws of electrodynamics can be illustrated by a series of
5 small experiments which show qualitatively the interrelationships of
electric and magnetic fields.
2
0
c (circulation of B around C) = (flux of E through S)
flux of electric current through S
+
d
dt


16. A bar magnet gives a fleld B at a wire.
When there is a current along the wire, the wire moves because
of the force F = qv × B.

17. How does the wire push on the magnet?
The current in the wire produces a
magnetic field of its own that exerts forces on the magnet.

18. Two wires, carrying current,
exert forces on each other.

19. The bar magnet can be replaced by a coil carrying an
electrical current. A similar force acts on the wire.

20. The circulation of B around the curve C
is given either by the current passing through
the surface S1, or by the rate of change of the
flux of E through the surface S2
.

21. • The small magnetism is of two kinds. Some materials are attracted
toward magnetic fields; others are repelled.
• Diamagnetic:
Repelled from high field region
e.g. Bismuth
• Paramagnetic:
Weak force towards pointed pole
e.g. Aluminium
5. Diamagnetism and Paramagnetism

22. Mechanism of Diamagnetism
• In many substances, atoms have no permanent magnetic moments.
Electron spins and orbital motions all exactly balance out, so atom
has no average magnetic moment.
• Turn on a magnetic field little extra currents are generated inside
the atom by induction.
• According to Lenz's law, these currents are in such a direction as to
oppose the increasing field. So the induced magnetic moments of
the atoms are directed opposite to the magnetic field.

23. Mechanism of Paramagnetism
• Some substances, atoms have permanent magnetic moments. Electron
spins and orbital motions have net non-zero circulating current.
• Diamagnetic effect (always present) + Effect of lining up the
individual atomic magnetic moments.
• Induced magnetism which enhances the existing field.
• Paramagnetism is weak because the lining-up forces are relatively
small compared with the forces from the thermal motions which try
to derange the order.

24. Ferroelectric material
• Ferroelectric material: In which all the electric dipoles get lined up
by their own mutual electric fields.
• Magnetic analogy of Ferro-electricity, in which all the atomic
moments would line up and lock together.
• But magnetic forces are so smaller than the electric forces, thermal
motions should knock out this alignment even at low temperatures.
• Not possible at room temperature to have any permanent lining up
of the magnets.

25. Ferroelectric material - IRON
• On the other hand, this is exactly what does happen in iron—it does
get lined up.
• There is an effective force between the magnetic moments of the
different atoms of iron which is much, much greater than the direct
magnetic interaction.
• It is an indirect effect which can be explained only by quantum
mechanics.
• It is about ten thousand times stronger than the direct magnetic
interaction, and is what lines up the moments in ferromagnetic
materials.

26. Quantum Mechanical Phenomenon
• It is not possible to understand the magnetic effects of materials in
any honest way from the point of view of classical physics.
• Such magnetic effects are a completely quantum-mechanical
phenomenon.
• However, it is possible to make some analogical arguments to get
some idea of what is going on.

27. Thank You