ELECTROMAGNETIC WAVES

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Oct 18, 2013 (3 years and 9 months ago)

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ELECTROMAGNETIC WAVES

(Important formulae and Concepts)




A

linearly polarized electromagnetic waves


Time varying magnetic field is a source of electric field, and time varying electric field is a source of


magnetic field. Time and space varying elect
ric and magnetic field produce the electromagnetic wave.


Polarized wave:

E.M wave having two components (E
y
,B
z
) or (E
z
,B
y
) .


Unpolarized wave:

E.M wave having both components (E
y
,B
z
) and (E
z
,B
y
).


Properties of Electromagnetic waves:



i) Time and space
varying electric & magnetic field produce the E.M wave.


ii) E.M waves are transfers in nature .


iii
) Velocity of E.M wave in a free space


c
0
=1/


0


0

iv
) E.M carries the energy


v) The magnetic energy density of E.M wave U
B

=B
0
2
/2



vi)

The Electric energy density of E.M wave U
E

=1/2

0
E
0
2


vii
) Average magnetic energy density <U
B
>=

B
0
2
/4

0


viii
) Average electric energy density <U
E
>=1/2

0
E
0
2


ix
) Total energy density of E.M.Wave = U
B
+

U
E


x
) In E.M wave optical effect is produced by elec
tric field so electric field is called light vector.



Uses of E.M Spectrum:


i)

Radio waves:

Its frequency range is 5X10
6

Hz to 10
9

Hz. These waves are used in a radio
and T.V broadcasting system and for communication.


ii)

Microwaves:

Its frequency range is 10
9

Hz to 10
11
Hz. These waves are used for a) Radar
communication b) to study atomic and nuclear research. c) in a aircraft navigation. d) in
micro wave ovens for cooking and warming of food


iii)

Infrared rays:

Its frequency ranger is 3X10
11

Hz to 4X10
14

Hz. The
se rays are used for i)
Taking photographs in clouds and foggy conditions. ii) in treatment of muscular strains. iii)
revealing the secret writings on ancient walls.


iv)

Visible radiations:

Its frequency range is 4X10
14

Hz to 7.5X10
14

Hz. These rays are used

in i) In photography ii) In optical microscopes iii) In astronomy.


v)

Ultra
-
violet rays:

Its frequency range is 7.5X10
14

Hz to 5X10
15

Hz. These rays are used
for i) To preserve the food stuffs ii) In making drinking water free from bacteria and germs
iii) I
n sterilizing surgical instruments iv) In detecting invisible writings, forged documents
and finger prints.


vi)

X
-
rays
: Its frequency range 10
15

Hz to 10
18

Hz. These rays are used in i) In medical
diagnosis ii) For locating faults and cracks in big metallic b
odies iii) In radio therapy to
cure skin diseases , cancers and tumors iv) In location body fractures v) To study the
crystal structure.


vii)


-
rays
: Its frequency range is 10
18
Hz to 10
22

Hz . These rays are used in i) Treatment of
cancer ii) To study the str
ucture of the nucleus.



1
marks questions


Q. 1. What is the approximate wavelength of X rays .


Q.2. Arrange the following electromagnetic radiations in the ascending order of the
w
avelength :


microwaves ,
ϒ

rays , radio waves , ultraviolet light


Q.3.Give one medical use of UV rays.


Q.4. Which of the following has the lowest frequency : microwave , UV rays and X
-

rays.


Q.5. What is the equation for the speed of electromagnetic waves in free space.


Q.6. What is the wavelength range of visib
le spectrum.


Q.7. Name the electromagnetic radiation to which the following wavelength belong


(a) 10
-
2

m (b) 1 Å


Q.8. Long distance radio broadcasts use short wave bands .why?


Q.9.What oscillates in electromagnetic waves ?


Q.10. Find the

wavelength of electromagnetic waves of frequency 4x10
9

Hz in free
s
pace.


Q.11. In electromagnetic waves infrared region lies between the radio wave and microwave region. Is


this statement correct ?


Q.12. What is the relation between amplitude o
f electric and magnetic fields in free

space for an


electromagnetic waves.


Q.13. The charging current for a capacitor is 0.25 A .What is the displacement current cross its plates.


Q.14. Which part of the electromagnetic spectrum has the largest

penetrating power?


Q.15. What is the ratio of speeds of infrared rays and ultraviolet rays in vacuum?


Q.16. Microwaves are used in Radar .Why?


Q.17. What is the cause of conduction current?


Q.18. What is the maxwell’s displacement current ?


Q.19. The

small ozone layer on the top of the stratosphere is crucial for human

survival .Why?


Q.20. State the part of the e.m. spectrum to which each belongs . 2.7 K temperature associated with


the isotropic radiation filling all space thought to be reli
c of the big bang
o
rigin of the universe.


Q.21.For which frequency of light , the human eye is most sensitive ?


Q.22. What is the role of ozone layer in the atmosphere ?


Q.23. Which layer of the earth’s atmosphere is useful in long distance radio transm
ission?


Q.24. What is the nature of the waves used in radar ? What is their wavelength range ?


Q.25. Name the part of the electromagnetic spectrum which is used in green houses to

keep plants


warm.


Q.26.

Give a reason to show that microwaves ar
e better carrier of signals for long range transmission


than radio waves ?


Q.27. What is common between different types of electromagnetic radiations ?


Q.28. What is the frequency range of microwaves ?


Q.29. State one use and one method of det
ecting the rays beyond the visible red end of the


electromagnetic spectrum.


Q.30.
Find the wavelength of the electromagnetic waves of frequency 5x
10
19
Hz






Two

& Three

marks questions


Q.3
1. Electromagnetic wave have wavelength


(i)

1

are used to kill germs in water purifiers.


(ii)

2

are used in aircraft navigation.


(iii)

3

are referred to as ‘heat waves.


Identify the waves and arrange them in ascending order of their magnitudes.


Q.3
2.

State any four
bas
ic
properties of electromagnetic waves.


Q.3
3.
Which of the following ,if any, can act as a source of electromagnetic waves
:


(i) A charge moving with a constant velocity.


(ii) A charge moving in a circular orbit.


(iii) A charge a
t rest.


Give reason.


Q.3
4. A plane electromagnetic wave travel ,in vacuum ,along the y

direction. Write (i) the ratio of


the magnitudes, and (ii) the directions of its ele
ctric and magnetic field vectors.

Q.3
5. A plane electromagnetic wave of frequency 25 MHz travel in free space along the x
-


direction .At a particular point in space and time E = 6.3 j V/m. What is B at this point.


Q.3
6.

Which part of the electr
omagnetic radiation:


(i)

is used for satellite communication


(ii)

has is frequency range 4 x 10
14

Hz to 7 x 10
14
Hz


(iii)
produce intense heating effect


(iv)
used for purification of water.

Q
.3
7.


The amplitude of electric fie
ld in an electromagnetic wave is E
o

= 120 N/C and its frequency is


ν = 50.0 MHz. (a) Determine, B
o
,ω, k, and λ. (b) Find expressions for
E
and
B.

Q.
3
8.
Suppose that the electric field part of an electromagnetic wave in

vacuum is



E
= {(3.1 N/C) cos [(1.8 rad/m)
y
+ (5.4 × 106 rad/s)
t
]}
ˆ
i
.



(a) What is the direction of propagation?



(b) What is the wavelength

?



(c) What is the frequency

?



(d) What is the amplitude of the magnetic field part of the wave?


Q.
3
9

Answer the following questions


(
i
) If the earth
did not have an atmosphere, would its average

surface temperature



be higher or lower than what it is now?


(ii
) Some scientists have predicted that a global nuclear war on theearth would be



followed by a severe ‘nuclear winter’
with a

devastating effect on life on earth.



What might be the basis of

this prediction?



(
iii
) Optical and radiotelescopes are built on the ground but X
-
ray

astronomy is



possible only from satellites orbiting the earth.Why?

Q.
4
0.

In a plane electromagnetic wave, the electric field oscillates

sinusoidally at a



frequency of 2.0 × 1010 Hz and amplitude 48 V m

1.



(a) What is the wavelength of the wave?


(b) What is the amplitude of the oscillating magnetic field?


(c) Show that the average energy density of the
E
field equals the


average energy density of the
B
field. [
c
= 3 × 108 m s

1.]








Electromagnetic Wave
( Additional Questions)
.


1.

What is displacement current? Write an expression for displacement current?
What modification was made by Maxwell in Ampere circuital law.

2.

For an E.M. wave write the relat
ionship between amplitued of Electric and
magnetic field in free space?

3.

Give a schematic and labelled diagram Hertz experiment for producing E.M.
Wave.

4.

Name the E.M radiation to which the following wave length belongs (i) 10
-
2

m.
(ii) 1A
0.

5.

What is the appr
oximate wav length of X ray?

6.

Which of the following has shortest wave length:
-

Micro wave, UV rays and X
ray arrange the following in the descending order of wave length:
-

Y ray, infra red ray, mirco wave,
yellow light radio wave.

7.

What is green house effec
t? Which layer of earth atmosphere protect us from
UV radiation coming from the sun.

8.

Write four characterstic of E.M wave.

9.

Give one uses of each of the following (i) Micro wave (ii) I.R wave (iii) U.V
radiation (iV) Gama ray.

10.

Identify the following E.M rad
iation as per the wave length given below. Write
one application of each (i) 1 mm (ii) 10
-
3nm
(iii) 10
-
8m
.

11.

Identify the following E.M radiation as per the frequency given below. Write
one application of each ( i) 10
20

HZ (ii) 10
9

HZ (iii) 10
11

HZ.

12.

Electrom
egnetic wave with wave length

(i)

λ
1
are used to treat to treat mascular strain (ii) λ
2

are used by F.M radio
station.

(ii)

Λ
3

are used to detect fracture in bone.

(iii)

Λ
4
are observed by ozone layer. Identify and name the part of E.M spectrum to
which these radiation belong.

(iv)

Arrange these wave le
ngth in decreasing order of magnitue.

13.

Name the constituent radiation of a E.M spectrum which (i) is used in setallite
communication.(ii) is used for studying crastal structure. (iii) is similar to the radiation emitted during
decay of radio active nuclei (
iv) Has a wave length wave length range between 390nm and 770 nm.
(v) is observed from sunlight by ozone layer (Vi) porduce intense heating affect.

14.

E.M radiation with wave length (i) λ
1

are used to kill germs in water purifier. (ii)
λ
2

are used T.V. communication. (iii) λ
3
play an important role in mainting the earth warm. Name the
part of E.M spectrum to which these radiation belong. Arrange these wa
ve length in decreasing order
of their magnetic.

15.

Write the order of frequency range and one used of each of the following E.M
radiation (i) Micro wave (ii) UV rays (iii) Gama rays.














Question 8.1:

Figure 8.6 shows a cap
acitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm.
The capacitor is being charged by an external source (not shown in the figure). The charging current is
constant and equal to 0.15 A.

(a)
Calculate the capacitance and the ra
te of charge of potential difference between the plates.

(b)
Obtain the displacement current across the plates.

(c)

Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.




Answer


Radius of each

circular plate,
r

= 12 cm = 0.12 m

Distance between the plates,
d

= 5 cm = 0.05 m

Charging current,
I

= 0.15 A

Permittivity of free space,
= 8.85 × 10

12

C
2

N

1

m

2

(a)

Capacitance between the two plates is given by the relation,

C


Where,

A

= Area of each plate


Charge on each plate,
q

=
CV

Where,

V = Potential difference across the plates

Differentiation on both sides with respect to time (
t
) g
ives:


Therefore, the change in potential difference between the plates is 1.87 ×10
9

V/s.

(b)

The displacement current across the plates is the same as the conduction current. Hence, the
displacement current,
i
d

is 0.15 A.

(c)
Yes

Kirchhoff’s first rule i
s valid at each plate of the capacitor provided that we take the sum of conduction and
displacement for current.

Question 8.2:

A parallel plate capacitor (Fig. 8.7) made of circular plates each of radius
R
= 6.0 cm has a capacitance
C
=
100 pF. The capacit
or is connected to a 230 V ac supply with a (angular) frequency of 300 rad s

1
.

(a)
What is the rms value of the conduction current?

(b)

Is the conduction current equal to the displacement current?

(c)
Determine the amplitude of
B
at a point 3.0 cm from th
e axis between the plates.




Answer


Radius of each circular plate,
R

= 6.0 cm = 0.06 m

Capacitance of a parallel plate capacitor,
C

= 100 pF = 100 × 10

12

F

Supply voltage,
V

= 230 V

Angular frequency,
ω

= 300 rad s

1

(a)

Rms va
lue of conduction current,
I


Where,

X
C

= Capacitive reactance




I

=
V

×
ωC

= 230 × 300 × 100 × 10

12

= 6.9 × 10

6

A

= 6.9 μA

Hence, the rms value of conduction current is 6.9 μA.

(b)

Yes, conduction current is equal to displacement current.

(c)

Magnet
ic field is given as:

B


Where,

μ
0

= Free space permeability

I
0

= Maximum value of current =

r

= Distance between the plates from the axis = 3.0 cm = 0.03 m


B


= 1.63 × 10

11

T

Hence, the magnetic field at that point is 1.63 × 10

11

T.

Question 8.3:

What physical quantity is the same for X
-
rays of wavelength 10

10

m, red light of wavelength 6800 Å and
radiowaves of wavelength 500 m?



Answer


The speed of light (3 × 10
8

m/s) in a vacuum is the same for all wavelengths. It is
independent of the
wavelength in the vacuum.

Question 8.4:

A plane electromagnetic wave travels in vacuum along z
-
direction. What can you say about the directions of
its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is i
ts wavelength?



Answer


The electromagnetic wave travels in a vacuum along the z
-
direction. The electric field (
E
) and the magnetic
field (
H
) are in the
x
-
y

plane. They are mutually perpendicular.

Frequency of the wave, ν = 30 MHz = 30 × 10
6

s

1

Speed of light in a vacuum,
c

= 3 × 10
8

m/s

Wavelength of a wave is given as:


Question 8.5:

A radio can tune in to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength
band?



Answer


A radio can tune to minimum frequency,
ν
1

= 7.5 MHz= 7.5 × 10
6

Hz

Maximum frequency,
ν
2

= 12 MHz = 12 × 10
6

Hz

Speed of light,
c

= 3 × 10
8

m/s

Corresponding wavelength for
ν
1

can be calculated as:


Corresponding wavelength

for
ν
2

can be calculated as:


Thus, the wavelength band of the radio is 40 m to 25 m.

Question 8.6:

A charged particle oscillates about its mean equilibrium position with a frequency of 10
9

Hz. What is the
frequency of the electromagnetic waves produced
by the oscillator?



Answer


The frequency of an electromagnetic wave produced by the oscillator is the same as that of a charged
particle oscillating about its mean position i.e., 10
9

Hz.

Question 8.7:

The amplitude of the magneti
c field part of a harmonic electromagnetic wave in vacuum is
B
0

= 510 nT.
What is the amplitude of the electric field part of the wave?



Answer


Amplitude of magnetic field of an electromagnetic wave in a vacuum,

B
0

= 510 nT = 51
0 × 10

9

T

Speed of light in a vacuum,
c

= 3 × 10
8

m/s

Amplitude of electric field of the electromagnetic wave is given by the relation,

E

=
cB
0

= 3 × 10
8
× 510 × 10

9
= 153 N/C

Therefore, the electric field part of the wave is 153 N/C.

Question 8.8:

Suppo
se that the electric field amplitude of an electromagnetic wave is
E
0

= 120 N/C and that its frequency
is
ν

= 50.0 MHz. (a) Determine,
B
0
,
ω,
k,
and λ. (b) Find expressions for
E
and
B
.



Answer


Electric field amplitude,
E
0

= 120
N/C

Frequency of source,
ν

= 50.0 MHz = 50 × 10
6

Hz

Speed of light,
c

= 3 × 10
8
m/s

(a)

Magnitude of magnetic field strength is given as:


Angular frequency of source is given as:

ω

= 2π
ν

= 2π × 50 × 10
6

= 3.14 × 10
8

rad/s

Propagation constant is given
as:


Wavelength of wave is given as:


(b)

Suppose the wave is propagating in the positive
x

direction. Then, the electric field vector will be in the
positive
y

direction and the magnetic field vector will be in the positive
z

direction. This is because

all three
vectors are mutually perpendicular.

Equation of electric field vector is given as:


And, magnetic field vector is given as:


Question 8.9:

The terminology of different parts of the electromagnetic spectrum is given in the text. Use the form
ula
E
=


(for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different
parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you
obtain related to the sources of ele
ctromagnetic radiation?



Answer


Energy of a photon is given as:


Where,

h

= Planck’s constant = 6.6 × 10

34

Js

c

= Speed of light = 3 × 10
8

m/s

λ = Wavelength of radiation


The given table lists the photon energies for diffe
rent parts of an electromagnetic spectrum for different
λ
.

λ
(m)

10
3

1

10

3

10

6

10

8

10

10

10

12

E
(eV)

12.375
× 10

10

12.375
× 10

7

12.375
× 10

4

12.375
× 10

1

12.375
× 10
1

12.375
× 10
3

12.375
× 10
5

The photon energies for the different parts of the spe
ctrum of a source indicate the spacing of the relevant
energy levels of the source.

Question 8.10:

In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 10
10

Hz and
amplitude 48 V m

1
.

(a)

What is the wavelengt
h of the wave?

(b)
What is the amplitude of the oscillating magnetic field?

(c)
Show that the average energy density of the
E
field equals the average energy density of the
B
field. [
c
= 3 × 10
8

m s

1
.]



Answer


Frequency of the e
lectromagnetic wave,
ν

= 2.0 × 10
10

Hz

Electric field amplitude,
E
0

= 48 V m

1

Speed of light,
c

= 3 × 10
8

m/s

(a)

Wavelength of a wave is given as:


(b)

Magnetic field strength is given as:


(c)

Energy density of the electric field is given as:


And
, energy density of the magnetic field is given as:


Where,


0

= Permittivity of free space

μ
0

= Permeability of free space

We have the relation connecting
E

and
B

as:

E

=
cB

… (1)

Where,

… (2)

Putting equation (2) in equation (1), we get


Squaring b
oth sides, we get