Em Waves Lec3,4,5

Ch 8-
Electromagnetic Waves
Lect-03
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Today’s Goal
Equation of Electric Field
& Magnetic Field in an
Electromagnetic Wave
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1. Electromagnetic Wave is radiated(produced) by an
accelerated (or oscillating) charge particle.
2. Electromagnetic Wave propagates in space through

Oscillations of Electric and Magnetic Field ,
perpendicular to each other and also perpendicular
to the direction of wave propagation.
3. Since the oscillation of Electric Field and Magnetic

Field occur perpendicular to direction of wave
propagation, EMW is a Transverse Wave
Equation of Electric Field
&
Equation of Magnetic Field

7
Brief Introduction to Travelling Wave

Displacement of particle(y)

Equation of Electromagnetic Waves
1. Electric Field 𝑬

2. Magnetic Field 𝑩

Q1) The electric field in a plane electromagnetic wave is
3 11 𝑵
given by Ey=2sin(0.5x 10 𝒙+1.5x10 t)
𝑪
a) What is the direction of propagation
b) Speed of wave

Peak Value of 𝑬 (𝑬𝒐) and 𝑩 (𝑩𝒐)

Q2) The magnetic field in the plane electromagnetic wave is
given by Bz=2x10-7 sin(0.5 x 103x +1.5 x 1011 t)tesla. The
expression for electric field will be
a) Ez=30 𝟐sin(0.5 x 103𝒙 + 1.5 x1011 t)V/m

b) Ez=60sin(0.5 x 103𝒙 + 0.5 x1011 t)V/m
c) Ey= 30 𝟐 sin(0.5 x 1011𝒙 + 0.5 x103 t)V/m
d) Ey= 60 sin(0.5 x 103𝒙 + 1.5 x1011 t)V/m

Q3)

Permeability & Permittivity of Medium
1. In air/vacuum/free space
2. In any other medium

Q4) If c is the speed of electromagnetic waves in vacuum ,its
speed in a medium of dielectric constant K and relative
permeability μr is
𝟏
a) 𝒗 =
𝝁𝒓𝑲
b) 𝒗 = 𝒄 𝝁𝒓𝑲
𝒄
c) 𝒗 =
𝝁𝒓𝑲
𝑲
d) 𝒗 =
𝝁𝒓𝑪

Q5) A plane electromagnetic wave Ez=100cos(6x108t +4x)
V/m propagates in a non magnetic medium of dielectric
constant
a) 1.5
b) 2.0
c) 2.4
d) 4.0

Q6) If 𝜺𝒐 and 𝝁𝒐 represent the permittivity and permeability
of vacuum 𝜺 and 𝝁 represent the permittivity and
permeability of medium, the refractive index of the medium
is given by
𝜺
a)
𝜺𝒐𝝁𝒐 c) 𝜺𝒐𝝁𝒐
𝜺𝝁
𝜺𝝁 𝜺𝒐𝝁𝒐
b) d) 𝜺
𝜺𝒐𝝁𝒐

Q6) An EM wave from air enters a medium. The electric
𝒛
ෝ𝒄𝒐𝒔[𝟐𝝅𝒗 − 𝒕 ] in air 𝑬𝟐 =
fields are 𝑬𝟏 = 𝑬𝟎𝟏𝒙
𝒄
𝑬𝟎𝟐𝒙ෝ𝒄𝒐𝒔[𝒌 𝟐𝒛 − 𝒄𝒕 ] in medium, where the wave number k
and frequency 𝒗 refer to their values in air. The medium is
non-magnetic . If 𝜺𝒓𝟏 and 𝜺𝒓𝟐 refer to relative permittivites of
air and medium respectively, which of the following options
is correct? [JEE MAIN 2018]
𝜺𝒓𝟏
a)
𝜺𝒓𝟏
=
𝟏 c) 𝜺𝒓𝟐
=𝟐
𝜺𝒓𝟐 𝟐 𝜺𝒓𝟏 𝟏
𝜺𝒓𝟏 d) =
b) 𝜺𝒓𝟐
=𝟒 𝜺𝒓𝟐 𝟒

Ch 8-
Lect-04
Today’s Goal
1. Energy Density
2. Intensity
3. Momentum
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Energy Density of ElectroMagnetic Waves
1. Electromagnetic Waves carry energy as they travel
through space. Thus Energy is contained in oscillating
Electric and Magnetic Field.
2. Equal amount of Energy is contributed by Electric and

Magnetic Field.
3. By now, we know that EMW are produced by

oscillating charge in L-C circuit. The energy of Electric
Field is from Capacitor(C) while Energy of Magnetic
Field is from Inductor (L)

Energy density of Electric Field (𝝁𝑬)

Energy density of Magnetic Field (𝝁𝑩)
𝒏 = 𝒏𝒐. 𝒐𝒇 𝒕𝒖𝒓𝒏𝒔
𝒑𝒆𝒓 𝒖𝒏𝒊𝒕 𝒍𝒆𝒏𝒈𝒕𝒉

Show that (𝝁𝑩) = (𝝁𝑬)

Total Energy density in Electromagnetic
Wave

Summary
𝟏 𝟏
𝝁𝒂𝒗𝒈 = 𝜺𝒐𝑬𝒐𝟐 = 𝑩𝒐𝟐
𝟐 𝟐𝝁𝒐
𝟏 𝟏
(𝝁𝑬)𝒂𝒗𝒈 = 𝝁𝒂𝒗𝒈 = 𝜺𝒐𝑬𝒐𝟐
𝟐 𝟒
𝟏 𝟏
(𝝁𝑩)𝒂𝒗𝒈 = 𝝁𝒂𝒗𝒈 = 𝜺𝒐𝑩𝒐𝟐
𝟐 𝟒

Q1) The magnetic field in a plane e.m.wave is given by 𝑩 =
−𝟓 −𝟏 𝒙
(𝟐𝟎𝟎𝝁𝑻)𝒔𝒊𝒏(𝟒. 𝟎 × 𝟏𝟎 𝒔 )(𝒕 − ) Find the average energy
𝒄
density corresponding to the electric field.
a) 16μ J/m3
b) 8μ J/m3
c) 4μ J/m3
d) 2μ J/m3

Q2) During the propagation of electromagnetic waves in a
medium: [JEE MAIN 2014]
a) Electric energy density is equal to the magnetic

energy density
b) Both electric and magnetic energy densities are
zero.
c) Electric energy density is double of the magnetic
energy density
d) Electric energy density is half of the magnetic
energy density
Intensity of an Electromagnetic Wave
The energy crossing per unit time in a direction
perpendicular to the direction of propagation is called
intensity of the wave.

Q3) A flood light is covered with a filter that transmits red
light. The electric field of the emerging beam is represented by
a sinusoidal plane wave Ex=20sin(1.20x107 z-3.6 x 1015 t)V/m.
The average intensity of beam in W/m2 will be
a) 6
b) 2
c) 1
d) 0.5

Relation between Power & Intensity

Q4) The sun delivers 104 W/m2 of electromagnetic flux to the
earth’s surface. The total power that is incident on a roof of
(10x10)m2 will be
a) 104 W
b) 105 W
c) 106 W
d) 107 W

Q5) A red LED emits light at 0.1 watt uniformly around it. The
amplitude of the electric field of the light at a distance of 1 m
from the diode is [JEE MAIN 2015]
a) 1.73 V/m
b) 2.45 V/m
c) 5.48 V/m
d) 7.75 V/m

Momentum of Electromagnetic Wave
De-Broglie hypothesis

Pointing Vector (𝑺)
𝑺 represents the direction of energy flow per unit
area per unit time along the direction of wave
propagation

Ch 8-
Lect-05
Today’s Goal
Properties of
Electromagnetic
Spectrum
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Properties of Electromagnetic Waves
➢The electromagnetic waves are produced by
accelerated charges and do not require any material
medium for their propagation.
➢The direction of oscillations of 𝑬 and 𝑩 fields are
perpendicular to each other as well as perpendicular
to the direction of propagation of waves so the
electromagnetic waves are transverse in nature.
➢The oscillations of 𝑬 and 𝑩 fields are in same phase.

➢All Electromagnetic waves travel in free space with
the same speed,
𝟏
c= ≈ 3 × 𝟏𝟎𝟖 m/s.
√𝝁∘𝟄∘
In material medium, the electromagnetic waves
travel with a speed,
𝟏 𝒄 𝒄
v= = =
√𝝁𝝐 √𝝁𝒓 𝝐𝒓 𝒏
where n is the refractive index of the medium.

➢The amplitude ratio of electric and magnetic field is
𝑬∘ 𝟏
=c= .
𝑩∘ √𝝁∘𝟄∘
➢The electromagnetic waves carry energy as they
travel through space and this energy is shared
equally by electric and magnetic field. The average
energy density of an e.m. wave is
u=

➢Electromagnetic waves transport linear momentum
as they travel through space.
𝑼
p=
𝒄
➢Electromagnetic Waves obey the principle of
superposition. They show the properties of
reflection,refraction, interference, diffraction and
polarisation .

➢The electric field of an electromagnetic waves is
responsible for its optical effects, because
𝑬𝟎 >> 𝑩𝟎

Electromagnetic Spectrum
The orderly distribution of the electromagnetic
waves in accordance with their wavelength or
frequency into distinct groups having widely
differing properties is called ELECTROMAGETIC
SPECTRUM.

1. Gamma Waves:
Wavelength Range: less than 10-3 nm
Production/Service: Radioactive decay of nucleus
Main Uses: Due to their high energy, they

1. Have strong penetrating power & hence are used to
kill Cancerous cells.
2. To preserve food stuffs for a long time because soft
Gamma rays can kill micro organism.

2. X-Rays:
Wavelength Range: 10-3 to 1nm
Production/Service: X-ray tubes or inner electrons
Main Uses: Medical diagnosis

1. Because X-rays can pass through flesh but not
through bones.
2. In the study of crystal structure.

3. Ultraviolet light (U.V. Waves)
Wavelength Range: 1nm to 400 nm
Production/Service: inner shell e- in atoms moving from one
energy level to a lower energy level.
Main Uses:
1. In food preservation as it has lethal effect on micro-
organism.
2. To detect alteration ghee because of its property of
florescence

4. Visible light
Wavelength Range: 400 nm to 700 nm
Production/Service: e- in an atoms emit light when they
move from one energy level to a lower energy level
Main Use:
Stimulates nerve ending of human eye.

5. Infrared Waves
Wavelength Range: 700 nm to 1mm
Production/Service: Vibration of atoms & molecules
Main Uses:
1. They are not scattered in fog or smoke, useful for
infra-red photographs or haze photography.
2. Used for therapeutic purposes.

6. Microwaves
Wavelength Range: 1mm to 0.1 m
Production/Service: Magnetron valve
Main Use:
1. Radar Communication.

7. Radiowaves
Wavelength Range: > 0.1 m
Production/Service: Rapid acceleration & deaccelerations of
e- in aerials.
Main Use:
1. Radio Communication.

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Ch 8-

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2. Electromagnetic Wave propagates in space through

3. Since the oscillation of Electric Field and Magnetic

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a) Ez=30 𝟐sin(0.5 x 103𝒙 + 1.5 x1011 t)V/m

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2. In any other medium

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2. Equal amount of Energy is contributed by Electric and

3. By now, we know that EMW are produced by

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a) Electric energy density is equal to the magnetic

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Main Uses: Due to their high energy, they

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Main Uses: Medical diagnosis

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