Electricity, Magnetism & Electro Magnetic Theory

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Nov 16, 2013 (3 years and 4 months ago)

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Electricity, Magnetism & Electro Magnetic Theory





1.

What is electricity? Explain its usefulness


Electricity

is a general term encompassing a variety of phenomena resulting from the presence and
flow of

electric charge
. These include many easily recognizable phenomena, such as

lightning
,

static
electricity
, and the flow of

electrical current

in an electrical wire. In addition, electrici
ty encompasses less
familiar concepts such as the

electromagnetic field

and

electromagnetic induction
.

The word is from the

New Latin

ēlectricus
, "amber
-
like"
[a]
, coined
in the year 1600 from the
Greek

ήλεκτρον

(electron) meaning

amber
, because electrical effects were produced classically by
rubbing amber.

In general usage, the word "electricity" adequately refe
rs to a number of physical effects. In a scientific
context, however, the term is vague, and these related, but distinct, concepts are better identified by more
precise terms:



Electric charge
: a property of some

subatomic particles
, which determines their

electromagnetic
interactions
. Electrically charged matter is influenced by, and produces, electromagnetic fields.



Electric current
: a movement or flow o
f electrically charged particles, typically measured
in

amperes
.



Electric field
: an influence produced by an
electric charge on other charges in its vicinity.



Electric potential
: the capacity of an electric field to do

work

on an

electric charge
, typically
measured in

volts
.



Electromagnetism
: a

fundamental interaction

between the magnetic field and t
he presence and
motion of an electric charge.

The most common use of the word "electricity" is less precise. It refers to:



Electric power

(which can refer imprecisely to a quan
tity of

electrical potential energy

or else more
correctly to electrical

energy per time
) that is provided commercially, by the

electrical power industry
.
In a loose but common use of the term, "electricity" may be used to

mean "wired for electricity" which
means a working

connection

to an electric

power
station
. Such a connection grants the user of
"electricity" access to the

electric field

present in

electrical wiring
, and thus to electric power.

Electrical phenomena have been studied since antiquity, though advances in the science were not made
until the seventeenth and eighteenth centuries. Practical applications for electricity however rem
ained
few, and it would not be until the late nineteenth century that

engineers

were able to put it to industrial
and residential use. The rapid expansion in el
ectrical technology at this time transformed industry and
society. Electricity's extraordinary versatility as a source of energy means it can be put to an almost
limitless set of applications which include

transport
,

heating
,

lighting
,
communications
, and

computation
.
Electrical power is the backbone of modern industrial society, and is expected to remain so for the
foreseeable
future.
[1]


2.

Write a note on the venin and Norton Theorem.


In

circuit theory
,

Thévenin's theorem

for

linear

electrical networks

states that any combination
of

voltage sources
,

current sources
, and

resistors

with two terminals is electrically equivalent to a single
voltage source

V

and a single s
eries resistor

R
. For single frequency AC systems the theorem can also
be applied to general

impedances
, not just resistors. The theorem was first discovered by Ger
man
scientist

Hermann von Helmholtz

in 1853,
[1]

but was then rediscovered in

1883 by
French

telegraph

engineer

Léon Charles Thévenin

(1857

1926).
[2]
[3]

This theorem states that a circuit of voltage sources and resistors can be converted into
a

Thévenin
equivalent
, which is a simplification technique used in circuit analysis. The Thévenin equivalent can be
used as a good model for a power supply or battery (with the resistor representing the

internal
impedance

and the source representing the

electromotive force
). The circuit consists of an ideal
voltage
source

in series with an ideal

resistor
.


Any

black box

containing only voltage sources, current sources, and other resistors can be converted to a Thévenin
equivalent circuit, comprising exactly one voltage source

and one resistor.




[
edit
]
Calculating the Thévenin equivalent

To calculate the equivalent
circuit, the resistance and voltage are needed, so

two equations

are required.
These two equations are usually obtained by using the following steps, but any
conditions placed on the
terminals of the circuit should also work:

1.

Calculate the output voltage,

V
AB
, when in

open circuit

condition (no

load resistor

meaning
infinite resistance). This is

V
Th
.

2.

Calculate the output current,

I
AB
, when the output terminals are

short circuited

(load resistance is
0).

R
Th

equals

V
Th

divided by this

I
AB
.

The equivalent circuit is a voltage source with voltage

V
Th

in series with a resistance

R
Th
.

Step 2 could also be thought of as:

2a. Replace voltage sources with
short circuits, and current sources with open circuits.

2b. Calculate the resistance between terminals A and B. This is

R
Th
.

The Thévenin
-
equivalent voltage is the voltage at the output terminals of the original circuit.
When calculating a Thévenin
-
equival
ent voltage, the

voltage divider

principle is often useful, by
declaring one terminal to be

V
out

and the other terminal to be at the ground point.

The Thévenin
-
equivalent res
istance is the resistance measured across points A and B "looking
back" into the circuit. It is important to first replace all voltage
-

and current
-
sources with their
internal resistances. For an ideal voltage source, this means replace the voltage source
with a
short circuit. For an ideal current source, this means replace the current source with an open
circuit. Resistance can then be calculated across the terminals using the formulae for

series and
parallel circuits
. This method is valid only for circuits with independent sources. If there
are

dependent sources

in th
e circuit, another method must be used such as connecting a test
source across A and B and calculating the voltage across or current through the test source.


3.

What is Gauss’s Theorem? Describe it with the help of some examples.


In

vector calculus
, the

divergence theorem
, also known as

Ostrogra
dsky
's theorem

[1]
, is a result
that relates the flow (that is,

flux
) of a

vector field

through a
surface

to the behavior of the vector field
inside the surface.

More precisely, the divergence

theorem states that the outward

flux

of a vector field through a closed
surface is equal to the

volume integral

o
f the

divergence

of the region inside the surface. Intuitively, it
states that

the sum of all sources minus the sum of all sinks gives the net flow out of a region
.

The divergence theo
rem is an important result for the mathematics of

engineering
, in particular
in

electrostatics

and

fluid dynamics
.

In physics and engineering, the divergence theorem is usually applied in three dimensions. However, it
generalizes to any number of dimensions. In one dimension, i
t is equivalent to the

fundamental theorem
of calculus
.

The theorem is a special case of the more general

Stokes' theorem
.
[2]




[
edit
]
Intuition

If a fluid is flowing in some area, and we wish to know how much fluid flows out of a certain region within
that ar
ea, then we need to add up the sources inside the region and subtract the sinks. The fluid flow is
represented by a vector field, and the vector field's divergence at a given point describes the strength of
the source or sink there. So, integrating the fie
ld's divergence over the interior of the region should equal
the integral of the vector field over the region's boundary. The divergence theorem says that this is true.

The divergence theorem is thus a

conservation law

which states that the volume total of all sinks and
sources, the volume integral of the divergence, is equal to the net flow across the volume's boundary.
[3]

[
edit
]
Mathematical statement



A region

V

bounded by the surface

S
=∂
V

with the
surface normal

n



The divergence theorem can be used to calculate a flux through a

closed surface

that fully encloses a volume, like any of
the surfaces on the left. It can
not

be used to calculate the flux through surfaces with boundaries, like those on the right.
(Surfaces are blue, boundaries are red.)

Suppose

V

is a subset of

R
n

(in the case of

n

= 3,

V

represents a volume in 3D space) which
is

compact

and has a

piecewise

smooth

boundary

S. If

F
is a continuously differentiable vector field
defined on a neighborhood of

V
, then we have


The left side is a

volume integral

over the volume

V
, the right side is the

surface integral

over the
boundary
of the volume

V
. The closed manifold ∂
V

is quite generally the boundary of

V

oriented by
outward
-
pointing

normals
, and

n

is the outward pointing unit normal field of the bounda
ry ∂
V
.
(d
S

may be used as a shorthand for

n

d
S
.) By the symbol within the two integrals it is stressed once
more that ∂
V

is a

closed

surface. In terms of the intuitive description above, the left
-
hand side of the
equation represents the total of the
sources in the volume

V
, and the right
-
hand side represents the
total flow across the boundary ∂
V
.


4.

What is optical fiber? Explain the types of optical fibers?


An

optical fiber (or optical fibre)

is a flexible, transparent fiber made of a pure glass (
silica
) not much
wider than a human hair. It functions as a

waveguide
, or "
light pipe
", to transmit light between the two
ends of the fiber.
[1]

The field of

applied science

and

engineering

concerned with the design and
application of optical fibers is known as

fiber optics
. Optical fibers are widely used in

fiber
-
optic
communications
, which permits transmission over longer distances and at higher

bandwidths

(data rates)
than other forms of communication. Fibers are used instead of metal wires because signals travel along
them with less

loss
and

are also immune to

electromagnetic interference
. Fibers are also used for
illumination, and are wrapped in bundles so they can be used to carry ima
ges, thus allowing viewing in
tight spaces. Specially designed fibers are used for a variety of other applications,
including

sensors

and

fiber lasers
.



An optical fiber junction box. The yellow cables are

single mode fibers
; the orange and blue cables are

multi
-
mode fibers
:
50/125 µm OM2 and 50/125 µm OM3 fibers respectively.

Optical fibers typically include a transparent

core

surrounded by a transparent

cladding

material with a
lower

index of refraction
. Light is kept in the core by
total internal reflection
. This causes the fiber to act
as
a

waveguide
. Fibers that support many propagation paths or

transverse modes

are cal
led

multi
-
mode
fibers

(MMF), while those that only support a single mode are called

single
-
mode fibers

(SMF). Multi
-
mode fibers generally have a larger core diameter, and are used for short
-
distance communication links
and for applications where high power must be transmitted. Single
-
mode fibers are used for most
communication links longe
r than 1,050 meters (3,440

ft).

Joining lengths of optical fiber is more complex than joining electrical wire or cable. The ends of the fibers
must be carefully

cleaved
, and th
en spliced together either

mechanically

or by

fusing

them together with
heat. Special

optical fiber connectors

for removable connections are also available.




[
edit
]
History



Daniel Colladon

first described this "light fountain" or "light pipe" in an 1842 article titled

On

the reflections of a ray of light
inside a parabolic liquid stream
. This particular illustration comes from a later article by Colladon, in 1884.

Fiber optics, though used extensively in the modern world, is a fairly simple and old technology. Guiding
of
light by refraction, the principle that makes fiber optics possible, was first demonstrated by

Daniel
Colladon

and

Jacques Babinet

in Paris in the early 1840s.

John Tyndall

included a demonstration of it in
his publ
ic lectures in London 12 years later.
[2]

Tyndall also wrote about the property of

total internal
reflection

in an introductory book about the nature of light in 1870: "When the light passes from air into
water, the refracted ray is bent

towards

the

p
erpendicular
... When the ray passes from water to air it is
bent

from
the perpendicular... If the angle which the ray in water encloses with the perpendicular to the
surface be greater than 48 degrees, the ray will not quit the water at all: it will be

tota
lly reflected

at the
surface.... The angle which marks the limit where total reflection begins is called the limiting angle of the
medium. For water this angle is 48°27', for flint glass it is 38°41', while for diamond it is
23°42'."
[3]
[4]

Unpigmented human hairs have also been shown to act as an optical fiber.
[5]

Practical applications, such as close internal illumination during dentistry, appeared early in the twentieth
century. Image transmission through tubes was demonstrated independe
ntly by the radio
experimenter

Clarence Hansell

and the television pioneer

John Logie Ba
ird

in the 1920s. The principle
was first used for internal medical examinations by

Heinrich Lamm

in the following decade. Modern
optical fibers, where the glass fiber is coated
with a transparent cladding to offer a more
suitable

refractive index
, appeared later in the decade.
[2]

Development then focused on fiber bundles for
image transmission.

Harold Hopkins
and

Narinder Singh Kapany

at

Imperial College

in London achieved
low
-
loss light transmission through a 75 cm long bundle which combined several thousand fibers.

Their
article titled "A flexible fibrescope, using static scanning" was published in the journal

Nature

in
1954.
[6]
[7]

The first fiber optic semi
-
flexible
gastroscope

was patented by

Basil Hirschowitz
, C. Wilbur
Peters, and Lawrence E. Curtiss, researchers at the

University of Michigan
, in 1956. I
n the process of
developing the gastroscope, Curtiss produced the first glass
-
clad fibers; previous optical fibers had relied
on air or impractical oils and waxes as the low
-
index cladding material.


5.

Explain the Concept of electric potential & also explain

relation between electric

potential
and electric field.


In

physics
, an

electric field

surrounds

electrically charged particles

and time
-
varying

magnetic fields
.
The electric field depicts the

force

exerted on other electrically charged objects by the electrically charged
particle the field is surrounding. The concept of an electric field was introduced by

Michae
l Faraday
.

The electric field is a

vector field

with

SI

units of

newtons

per

coulomb

(N C
−1
) or,
equivalently,

volts

per

metre

(V m
−1
). The SI base units of the electric field are kg∙m∙s
−3
∙A
−1
. The

strength
or magnitude

of the field at

a given point is defined as the force that would be exerted on a positive

test
charge

of 1 coulomb placed at that point; the direction of the field is given by the direction of that

force.
Electric fields contain

electrical energy

with

energy density

proportional to the
square of the field
amplitude. The electric field is to charge as gravitational

acceleration

is to mass and

force density

is to
volume.

An electric field that changes with time, such as due to the motion of charged particles in the field,
influences the local magnetic field. That is, the

electric and magnetic fields are not completely separate
phenomena; what one observer perceives as an electric field, another observer in a different

frame of
referenc
e

perceives as a mixture of electric and magnetic fields. For this reason, one speaks of
"
electromagnetism
" or "
electromagnetic fields
". In

quantum electrodynamics
, disturbances in the
electromagnetic fields are called

photons
, and the energy of photons is quantized.


6.

Explain the Boundary conditions for E and D at the interface of two homogeneous isotropic
dielectrics.

7.

Write a detail note on the applications of Ampere’s law.

8.

Explain the working principle of Ballistic Galvanometer.


A resonant ballistic galvanometer has been developed especially for precise magnetic flux measurements.
The sensitivity is high, one millimeter deflection at one meter scale distance corresponding to 4 Maxwell turns as
compared with 500 Maxwell turns for t
he same deflection in commercial galvanometers. The galvanometer is
based upon the principle stated by Maxwell that, if the charge to be measured by a ballistic galvanometer can be
sent repeatedly through the galvanometer in proper phase, the amplitude of
the swings will increase to a steady
value which is proportional to the charge and which is greater the smaller the damping. Operating the moving
coil in high vacuum eliminates air damping. A flat tape suspension, thin enough to approach in its properties
a
simple bifilar suspension, reduces elastic hysteresis. Light from the galvanometer mirror acts on a photoelectric
cell controlling the switching mechanism, to ensure the correct timing of the repeated impulses. A high accuracy
of integration is attained
by reducing to a minimum the eddy currents and hysteresis losses in the galvanometer
itself. This is done by avoiding the use of metal in the neighborhood of the coil.

A

ballistic galvanometer

is a type of

mirror galvanometer
. Unlike a current
-
measuring galvanometer, the
moving part has a large

moment of inertia
, thus giving it a long

oscillation

period. It is really
an

integrator

measuring the quantity of

charge

discharged through it. It can be either of the moving coil or
moving magnet type.

Before first use the ballistic constant of the galvanometer must be determined. This is usually done by
connecting to the galvanometer a
known
capacitor
, charged to a known

voltage

and recording the
deflection. The constant K is calculated from the

capacitance

C, the voltage V and the deflection d:

K

=

CV

/

d

where K is expressed in

coulombs

per centimeter.

In op
eration the unknown quantity of charge Q (in coulombs) is simply:

Q

=

kd
.

[
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]
Grassot Fluxmeter

An interesting form of ballistic galvanometer is the Grassot fluxmeter. In order to operate correctly, the
discharge time through the regular ballistic galvanometer must be shorter than the period of oscillation.
For some applications, especially those inv
olving inductors, this condition cannot be met. The Grassot
fluxmeter solves this. Its construction is similar to that of a ballistic galvanometer, but its coil is suspended
without any restoring forces in the suspension thread or in the current leads. The

core (bobbin) of the coil
is of a non
-
conductive material. When an electric charge is connected to the instrument, the coil starts
moving in the magnetic field of the galvanometer's magnet, generating an opposing

e.m.f.

and coming to
a stop regardless of the time of the current flow. The change in the coil position is proportional only to the
quantity of charge. The coil is returned to the zero position by the reversing of the current or manua
lly.