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ROLL NO.-
SESSION-
CLASS- UNDER THE SUPERVISION OF
MR. F. B. KANTH
This is to certify that project has been
Completed solely and satisfactory by this student
Going through original and genuine research work
Carried out to investigate about the subject matter as
Prescribed by CBSE.
NAME:-
ROLL NO:-
CLASS:-
SESSION:-
E= = (3)
0 0
This field is perpendicular to the surface S in figure (c). It has the same magnitude over the area A of
the capacitor plates.
Using Gauss’s law, the electric flux through the surface S is given by
𝐸= EA = A
0
(or) 𝐸= (4)
0
Since the charge Q on the capacitor plates changes with time, there is a current i which is given by
i=
dQ
dt
𝐸 i(5)
(or) 0 =
This is the missing term in Ampere’s circuital law.
The current given by equn (5) is due to changing electric field (or electric displacement ). Hence, it is called
‘Displacement Current’.
The current carried by conductors due to flow of charges is called conduction current’.
‘
The source of a magnetic field is not just the conduction electric current due to flowing charges, but
also the time rate of change of electric field. The total current i is the sum of the conduction current
𝐸 denoted
i= 𝑐+ 𝑑= 𝑐+ 0 (6)
Outside the capacitor plates, we have only conduction current 𝑐 = i, and no displacement current, i.e., 𝑑 = 0. On the
other hand, inside the capacitor, there is no conduction current, i.e., 𝑐 = 0, and there is only displacement current, so that
𝑑 = i. Hence, B at a point P outside the plates is the same at a point M between the plates.
(or) ׯ = 0( 𝑐+ 𝑑)
(or) ׯ = 0 𝑐
d 𝜙
0 dt 𝐸 (7) This
MAXWELL’S EQUATIONS:
4. ׯ = 0𝑐 0
𝐸 Ampere-Maxwell law
SOURCES OF ELECTROMAGNETIC WAVES:
accelerating charge ).This produces an oscillating electric field
Consider a charge oscillating with some frequency ( in space, which produces an oscillating magnetic field, which
in turn, is a source of oscillating electric field, and so on. The oscillating electric and magnetic fields thus regenerate
each other, as the wave propagates through the space . The frequency of the electromagnetic wave naturally equals
the frequency of oscillation of the charge. The energy associated with the propagating wave comes at the expense of
the energy of thesource – the accelerated charge.
From Maxwell’s equations, it is found that electric and magnetic fields in an electromagnetic wave are
perpendicular to each other, and to the direction of propagation. A typical example of a plane electromagnetic wave
propagating along the z direction(the fields are shown as a function of the z coordinate, at a given time t). The
electric field 𝒙 is along the x-axis, and varies sinusoidally with z, at a given time. The magnetic field 𝒚 is along the
y-axis, and again varies sinusoidally with z. The electric and magnetic fields 𝒙 and 𝒚 are perpendicular to each
other, and to the direction z of propagation.
E Electric Field ( along
X-axis ) B Magnetic
Field ( along Y- axis )
Electromagnetic Waves
along Z-axis
We can write 𝒙 and 𝒚 as follows:
where, k = magnitude of the wave vector (or) propagation vector. Its direction describes
the direction of
Since = and k = , c= =
(or) c= (4)
Also, it can be shown that
(5)
0=
0
(3) In an electromagnetic wave, the electric ( ) and magnetic ( ) field vectors are at right angles to each other and to
the direction of propagation. Hence electromagnetic waves are transverse in nature.
= 1.
𝜇0𝜀0
and the energy density associated with magnetic field is 𝑩𝟐 , there is a non zero energy density
𝟐𝝁𝟎
(10) Electromagnetic waves are not deflected by electric and magnetic fields.
ELECTROMAGNETIC SPECTRUM:
Electromagnetic spectrum is an orderly distribution of electromagnetic waves in terms of wavelength or frequency
Electromagnetic spectrum covers a wide range of wavelengths (or) frequencies. There is no sharp division between one
kind of wave and the next. The overlapping in certain parts of the spectrum shows that the particular wave can be
produced by different methods. We briefly describe these different types of electromagnetic waves, in order of decreasing
wavelengths or increasing frequencies.
1. Radio waves
2. Micro waves
3. Infra red waves
4. Visible rays
5. Ultra violet rays
6. X-rays
7. Gamma rays
RADIO WAVES :
(1) Radio waves are produced by the accelerated motion of
charges in conducting wires.
(4) The AM (amplitude modulated) band is from 530 kHz to 1710 kHz.
(5) Higher frequencies upto 54 MHz are used for short wave bands.
(7) The FM (frequency modulated) radio band extends from 88 MHz to 108 MHz.
(8) Cellular phones use radio waves to transmit voice communication in the ultrahigh frequency (UHF) band.
MICRO WAVES:
(1) Microwaves are short-wavelength radio waves, with frequencies in the gigahertz (GHz) range.
(2) They are produced by special vacuum tubes (called klystrons, magnetrons and Gunn diodes).
(3) Due to their short wavelengths, they are suitable for the radar systems used in aircraft navigation.
(4) Radar also provides the basis for the speed guns used to time fast balls, tennis serves, and automobiles.
(5) Micro waves are used in very long distance wireless communication through satellites.
(6) Micro waves are used in micro wave oven to cook food.
Working: It is used to cook the food in a short time. When the oven is operated, the microwaves are generated, which in
turn produce a non−uniform oscillating electric field. The water molecules in the food which are the electric dipoles are
excited by an oscillating torque. Hence few bonds in the water molecules are broken, and heat energy is produced. This is
used to cook food.
INFRA RED WAVES:
(1) Infrared waves are produced by hot bodies and molecules.
(2) This band lies adjacent to the low-frequency or long-wave length end of the visible spectrum.
(6) Infrared detectors are used in Earth satellites, both for military purposes and to observe growth of crops.
(7) Electronic devices (for example semiconductor light emitting diodes) also emit infrared and are widely used in
theremote switches of household electronic systems such as TV sets, video recorders and hi-fi systems.
VISIBLE RAYS:
(1) It is the part of the spectrum that is detected by the human eye.
(2) Its frequency ranges from about 4 × 14 Hz to about 7 × 14 Hz or a wavelength range of about 700 nm to 400 nm.
(3) Visible light emitted or reflected from objects around us provides us information about the world.(4) It is produced by
incandescent bodies
ULTRA VIOLET RAYS:
(1) It covers wavelengths ranging from about 4 × −7 m (400 nm) down to 6 × −10 m (0.6 nm).
(2) Ultraviolet (UV) radiation is produced by special lamps and very hot bodies.
(6) Due to its shorter wavelengths, UV radiations can be focussed into very narrow beams for high precision applications
such as LASIK () eye surgery. Laser assisted in situ kerato mileusis
(2) It covers wavelengths from about −8 m (10 nm) down to −13 m ( −4 nm).
(3) X-rays are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer.
(5) One common way to generate X-rays is to bombard a metal target by high energy electrons.
GAMMA RAYS:
(1) They lie in the upper frequency range of the electromagnetic spectrum and have wavelengths from about −10 m to
(2) They are the high frequency radiation produced in nuclear reactions and also emitted by radioactive nuclei..