ELECTROMAGNETIC WAVES FOR CBSE XII

CBSE NOTES; XII PHYSICS NOTES;BOARD NOTES;ELECTROMAGNETIC WAVES NOTES; PHYSICS NOTES FROM KOTA RAJASTAHN;
NOTES FROM KOTA COACHING;PHYSICS NOTES FROM AARAV CLASSES

1. PHYSICS
We Create Future in the Present
Chapter-8
ElectromagneticWaves
(2016-17)

2. S.NO.TOPIC PAGE NO.
1 THEORY…………………………………. …………………………………… 1-11
2 EXERCISE–I…………………………………………………. ……………1 2–13
3 EXERCISE–II……………………………………………………………… .14-14
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3. ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 1
Maxwell formulated a set of equations involving electric and magnetic fields, and their sources, the charge
and current densities. These equations are known as Maxwell’s equations. Togetherwith the Lorentz force
formula, they mathematically express all the basic laws of electromagnetism.The most important prediction to
emerge from Maxwell’s equations is the existence of electromagnetic waves, which are (coupled) time varying
electric and magnetic fields that propagate in space.
In this chapter, we first discuss the need for displacement current and its consequences. Then we present a
descriptive account of electromagnetic waves.Next we will discuss about the generation of electromagnetic
waves and its properties.The broad spectrum of electromagnetic waves, stretching fromg rays (wavelength
~10
–12
m) to longradiowaves (wavelength ~10
6
m) is described.
According toFaraday's law of inductionchanging magnetic flux induces an electric field
F
= -ò

 
B
d
E d
dt
(Faraday's law of induction)………………… (1)
HereE

is the electric field induced along a closed loop by the changing magnetic flux
B
Fin theregion
encircled by that loop.
Moreover, the equation governing the induction of a magnetic fieldis almost similar to above Equation.
F
= m eò

 
E
0 0
d
B d
dt
(Maxwell's law of induction)……………. (2)
HereB

is the magnetic field induced along a closed loop by the changing electric flux
E
Fin the region
encircled by that loop.
As an example, we consider the charging of a parallel-plate capacitor with circular plates. We assume that
the charge on our capacitorisbeing increased at a steady rate by a constant currentIin the connecting
wires.In such case the electric field magnitude between the plates must also be increasingat a steady rate.
Figure(b) is a view of the right-hand plate of Fig.(a)from between the plates. The electricfield is directed into
the page. Let us consider a circular loop through point 1 in Figs.(a)and(b). We assume this loop to be
concentric with the capacitor plates andhaving a radius smaller thanthat of the plates. Because the electric
field through the loop is changing, the electric flux throughthe loop must also be changing. According to
Maxwell, this changing electric flux induces a magnetic field around the loop.
ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 1
Maxwell formulated a set of equations involving electric and magnetic fields, and their sources, the charge
and current densities. These equations are known as Maxwell’s equations. Togetherwith the Lorentz force
formula, they mathematically express all the basic laws of electromagnetism.The most important prediction to
emerge from Maxwell’s equations is the existence of electromagnetic waves, which are (coupled) time varying
electric and magnetic fields that propagate in space.
In this chapter, we first discuss the need for displacement current and its consequences. Then we present a
descriptive account of electromagnetic waves.Next we will discuss about the generation of electromagnetic
waves and its properties.The broad spectrum of electromagnetic waves, stretching fromg rays (wavelength
~10
–12
m) to longradiowaves (wavelength ~10
6
m) is described.
According toFaraday's law of inductionchanging magnetic flux induces an electric field
F
= -ò

 
B
d
E d
dt
(Faraday's law of induction)………………… (1)
HereE

is the electric field induced along a closed loop by the changing magnetic flux
B
Fin theregion
encircled by that loop.
Moreover, the equation governing the induction of a magnetic fieldis almost similar to above Equation.
F
= m eò

 
E
0 0
d
B d
dt
(Maxwell's law of induction)……………. (2)
HereB

is the magnetic field induced along a closed loop by the changing electric flux
E
Fin the region
encircled by that loop.
As an example, we consider the charging of a parallel-plate capacitor with circular plates. We assume that
the charge on our capacitorisbeing increased at a steady rate by a constant currentIin the connecting
wires.In such case the electric field magnitude between the plates must also be increasingat a steady rate.
Figure(b) is a view of the right-hand plate of Fig.(a)from between the plates. The electricfield is directed into
the page. Let us consider a circular loop through point 1 in Figs.(a)and(b). We assume this loop to be
concentric with the capacitor plates andhaving a radius smaller thanthat of the plates. Because the electric
field through the loop is changing, the electric flux throughthe loop must also be changing. According to
Maxwell, this changing electric flux induces a magnetic field around the loop.
ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 1
Maxwell formulated a set of equations involving electric and magnetic fields, and their sources, the charge
and current densities. These equations are known as Maxwell’s equations. Togetherwith the Lorentz force
formula, they mathematically express all the basic laws of electromagnetism.The most important prediction to
emerge from Maxwell’s equations is the existence of electromagnetic waves, which are (coupled) time varying
electric and magnetic fields that propagate in space.
In this chapter, we first discuss the need for displacement current and its consequences. Then we present a
descriptive account of electromagnetic waves.Next we will discuss about the generation of electromagnetic
waves and its properties.The broad spectrum of electromagnetic waves, stretching fromg rays (wavelength
~10
–12
m) to longradiowaves (wavelength ~10
6
m) is described.
According toFaraday's law of inductionchanging magnetic flux induces an electric field
F
= -ò

 
B
d
E d
dt
(Faraday's law of induction)………………… (1)
HereE

is the electric field induced along a closed loop by the changing magnetic flux
B
Fin theregion
encircled by that loop.
Moreover, the equation governing the induction of a magnetic fieldis almost similar to above Equation.
F
= m eò

 
E
0 0
d
B d
dt
(Maxwell's law of induction)……………. (2)
HereB

is the magnetic field induced along a closed loop by the changing electric flux
E
Fin the region
encircled by that loop.
As an example, we consider the charging of a parallel-plate capacitor with circular plates. We assume that
the charge on our capacitorisbeing increased at a steady rate by a constant currentIin the connecting
wires.In such case the electric field magnitude between the plates must also be increasingat a steady rate.
Figure(b) is a view of the right-hand plate of Fig.(a)from between the plates. The electricfield is directed into
the page. Let us consider a circular loop through point 1 in Figs.(a)and(b). We assume this loop to be
concentric with the capacitor plates andhaving a radius smaller thanthat of the plates. Because the electric
field through the loop is changing, the electric flux throughthe loop must also be changing. According to
Maxwell, this changing electric flux induces a magnetic field around the loop.

4. ELECTROMAGNETIC WAVES
2 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
Experiments prove that a magnetic fieldB

is indeed induced around such a loop, directedas shown. This
magnetic field has the same magnitude at every point around the loop and thushasacircular symmetry
about thecentral axisof the capacitor plates (the axis extending from oneplate center to the other).If we now
consider a larger loop–say, through point 2 outside the platesin Figs.(a)and (b),we find that a magnetic
field is induced around that loop as well. Thus, whilethe electric field is changing, magnetic fields are induced
between the plates of a parallel-platecapacitor, both inside and outside the gap. When the electric field stops
changing, these inducedmagnetic fields disappear.
Although Eq.(1) is similar to Eq. (2), the equations differ in two ways.
1.Equation (2) has the two extra symbols
0
mand
0
e,but they appear only because we employ SIunits.
2.Equation (2) lacks the minus sign of Eq. (1), meaning that the induced electric fieldE

and theinduced
magnetic fieldB

have opposite directions when they are produced in otherwise similarsituations.
AMPERE-MAXWELL LAW
Now recall that the left side of Eq. (2), the integral of the dot product

 B daround a closed loop,appears in
another equation namely, Ampere's law:
= m Iò

  0 enc
B d (Ampere's law) …(3)
where lencis the current encircled by the closed loop. Thus, our two equations that specify the magnetic field
B

produced by means other than a magnetic material (i.e., by a current and by achanging electric field) give
the field in exactlythe same form. We can combine the two equationsinto the single equation as
F
= m e + m Iò

 
E
0 0 0 enc
d
B d
dt
(Ampere–Maxwell law)… (4)
When there is a current but no change in electric flux (such as with a wire carrying a constantcurrent), the first
term on theright side of Eq. (4) is zero, and so Eq. (4) reduces to Eq. (3), whichis Ampere's law. When there is a
change in electric flux but no current (such as inside or outside thegap of a charging capacitor), the second term
on the right side of Eq. (4) is zero, and so Eq. (4)reduces to Eq. (2), which is Maxwell's law of induction.
ELECTROMAGNETIC WAVES
2 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
Experiments prove that a magnetic fieldB

is indeed induced around such a loop, directedas shown. This
magnetic field has the same magnitude at every point around the loop and thushasacircular symmetry
about thecentral axisof the capacitor plates (the axis extending from oneplate center to the other).If we now
consider a larger loop–say, through point 2 outside the platesin Figs.(a)and (b),we find that a magnetic
field is induced around that loop as well. Thus, whilethe electric field is changing, magnetic fields are induced
between the plates of a parallel-platecapacitor, both inside and outside the gap. When the electric field stops
changing, these inducedmagnetic fields disappear.
Although Eq.(1) is similar to Eq. (2), the equations differ in two ways.
1.Equation (2) has the two extra symbols
0
mand
0
e,but they appear only because we employ SIunits.
2.Equation (2) lacks the minus sign of Eq. (1), meaning that the induced electric fieldE

and theinduced
magnetic fieldB

have opposite directions when they are produced in otherwise similarsituations.
AMPERE-MAXWELL LAW
Now recall that the left side of Eq. (2), the integral of the dot product

 B daround a closed loop,appears in
another equation namely, Ampere's law:
= m Iò

  0 enc
B d (Ampere's law) …(3)
where lencis the current encircled by the closed loop. Thus, our two equations that specify the magnetic field
B

produced by means other than a magnetic material (i.e., by a current and by achanging electric field) give
the field in exactlythe same form. We can combine the two equationsinto the single equation as
F
= m e + m Iò

 
E
0 0 0 enc
d
B d
dt
(Ampere–Maxwell law)… (4)
When there is a current but no change in electric flux (such as with a wire carrying a constantcurrent), the first
term on theright side of Eq. (4) is zero, and so Eq. (4) reduces to Eq. (3), whichis Ampere's law. When there is a
change in electric flux but no current (such as inside or outside thegap of a charging capacitor), the second term
on the right side of Eq. (4) is zero, and so Eq. (4)reduces to Eq. (2), which is Maxwell's law of induction.
ELECTROMAGNETIC WAVES
2 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
Experiments prove that a magnetic fieldB

is indeed induced around such a loop, directedas shown. This
magnetic field has the same magnitude at every point around the loop and thushasacircular symmetry
about thecentral axisof the capacitor plates (the axis extending from oneplate center to the other).If we now
consider a larger loop–say, through point 2 outside the platesin Figs.(a)and (b),we find that a magnetic
field is induced around that loop as well. Thus, whilethe electric field is changing, magnetic fields are induced
between the plates of a parallel-platecapacitor, both inside and outside the gap. When the electric field stops
changing, these inducedmagnetic fields disappear.
Although Eq.(1) is similar to Eq. (2), the equations differ in two ways.
1.Equation (2) has the two extra symbols
0
mand
0
e,but they appear only because we employ SIunits.
2.Equation (2) lacks the minus sign of Eq. (1), meaning that the induced electric fieldE

and theinduced
magnetic fieldB

have opposite directions when they are produced in otherwise similarsituations.
AMPERE-MAXWELL LAW
Now recall that the left side of Eq. (2), the integral of the dot product

 B daround a closed loop,appears in
another equation namely, Ampere's law:
= m Iò

  0 enc
B d (Ampere's law) …(3)
where lencis the current encircled by the closed loop. Thus, our two equations that specify the magnetic field
B

produced by means other than a magnetic material (i.e., by a current and by achanging electric field) give
the field in exactlythe same form. We can combine the two equationsinto the single equation as
F
= m e + m Iò

 
E
0 0 0 enc
d
B d
dt
(Ampere–Maxwell law)… (4)
When there is a current but no change in electric flux (such as with a wire carrying a constantcurrent), the first
term on theright side of Eq. (4) is zero, and so Eq. (4) reduces to Eq. (3), whichis Ampere's law. When there is a
change in electric flux but no current (such as inside or outside thegap of a charging capacitor), the second term
on the right side of Eq. (4) is zero, and so Eq. (4)reduces to Eq. (2), which is Maxwell's law of induction.

5. ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 3
DISPLACEMENT CURRENT
The current which comes into play in the region in which the electric field and the electric flux are
changing with time is known asdisplacementcurrent.
F
I = e
d 0
d
dt
(Displacementcurrent)………..(5)
On the behalf of displacement current
= m I + Iò

  0 d c enc
B d ( ) (Ampere–Maxwell law)
whereIdis the displacement current that is encircled by the integration loop andI
c
is the conduction
current which is carried by conductors due to flow of charges.
The real currentIin charging capacitor with circular plates that is charging the plates changes the electric field
E

between the plates. The fictitious displacement currentIdbetween the plates is associated with that
changing fieldE

.Let us relate these twocurrents.
The chargeqon the platesat any time is related to the magnitudeE ofthe field between theplates at that time
by the relation:
0
q AE,= e
whereA=plate area, On differentiating above equation
= I = e
0
dq dE
A .
dt dt
........................ (6)
To get the displacementcurrentI
d
, we can use Eq. (5). Assuming that the electric fieldE

betweenthe two
plates is uniform, we can replace the electric flux
E
Fin Eq. (5) with EA. Then
F °
I = e = e ´ = e ´
E
d 0 0 0
d d(EAcos0 ) dE
A .
dt dt dt
We know that the current carried by conductors due to flow of charges is calledconductioncurrent. The
current due to a changing electric field is known as Maxwell'sdisplacement current.
Wecan seeby Eqs.(5) and (6)that the real currentIcharging the capacitor and the fictitious displacement
currentIdbetween the plates have the same magnitude:
ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 3
DISPLACEMENT CURRENT
The current which comes into play in the region in which the electric field and the electric flux are
changing with time is known asdisplacementcurrent.
F
I = e
d 0
d
dt
(Displacementcurrent)………..(5)
On the behalf of displacement current
= m I + Iò

  0 d c enc
B d ( ) (Ampere–Maxwell law)
whereIdis the displacement current that is encircled by the integration loop andI
c
is the conduction
current which is carried by conductors due to flow of charges.
The real currentIin charging capacitor with circular plates that is charging the plates changes the electric field
E

between the plates. The fictitious displacement currentIdbetween the plates is associated with that
changing fieldE

.Let us relate these twocurrents.
The chargeqon the platesat any time is related to the magnitudeE ofthe field between theplates at that time
by the relation:
0
q AE,= e
whereA=plate area, On differentiating above equation
= I = e
0
dq dE
A .
dt dt
........................ (6)
To get the displacementcurrentI
d
, we can use Eq. (5). Assuming that the electric fieldE

betweenthe two
plates is uniform, we can replace the electric flux
E
Fin Eq. (5) with EA. Then
F °
I = e = e ´ = e ´
E
d 0 0 0
d d(EAcos0 ) dE
A .
dt dt dt
We know that the current carried by conductors due to flow of charges is calledconductioncurrent. The
current due to a changing electric field is known as Maxwell'sdisplacement current.
Wecan seeby Eqs.(5) and (6)that the real currentIcharging the capacitor and the fictitious displacement
currentIdbetween the plates have the same magnitude:
ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 3
DISPLACEMENT CURRENT
The current which comes into play in the region in which the electric field and the electric flux are
changing with time is known asdisplacementcurrent.
F
I = e
d 0
d
dt
(Displacementcurrent)………..(5)
On the behalf of displacement current
= m I + Iò

  0 d c enc
B d ( ) (Ampere–Maxwell law)
whereIdis the displacement current that is encircled by the integration loop andI
c
is the conduction
current which is carried by conductors due to flow of charges.
The real currentIin charging capacitor with circular plates that is charging the plates changes the electric field
E

between the plates. The fictitious displacement currentIdbetween the plates is associated with that
changing fieldE

.Let us relate these twocurrents.
The chargeqon the platesat any time is related to the magnitudeE ofthe field between theplates at that time
by the relation:
0
q AE,= e
whereA=plate area, On differentiating above equation
= I = e
0
dq dE
A .
dt dt
........................ (6)
To get the displacementcurrentI
d
, we can use Eq. (5). Assuming that the electric fieldE

betweenthe two
plates is uniform, we can replace the electric flux
E
Fin Eq. (5) with EA. Then
F °
I = e = e ´ = e ´
E
d 0 0 0
d d(EAcos0 ) dE
A .
dt dt dt
We know that the current carried by conductors due to flow of charges is calledconductioncurrent. The
current due to a changing electric field is known as Maxwell'sdisplacement current.
Wecan seeby Eqs.(5) and (6)that the real currentIcharging the capacitor and the fictitious displacement
currentIdbetween the plates have the same magnitude:

6. ELECTROMAGNETIC WAVES
4 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
Id=I(displacement current in a capacitor).
Thus, we can consider the fictitious displacement currentIdto be simply a continuation of the realcurrentI
from one plate, across the capacitor gap, to the other plate. Because the electric field isuniformly spread over
the plates, the same is true of this fictitious displacement currentId.
MAXWELL'S EQUATIONS
Discussion of the significance of Maxwell's equations
1.Maxwell's first equation:
The equation, whichis Gauss's law in electrostatics, gives us the valueof total electric flux due to charge
enclosed by a surface. This equation gives us information about the electric field due to discrete charges or
due to a certain charge distribution.It also indicatesthat electric lines of force start from a positive charge and
end at a negative charge.In other words, the electric lines of force do not form a continuous closed path. The
property that electric lines of force do not form a continuous closed path predicts the existence of isolated
electric charges.
=
e
ò
 

0
Q
E dA
2.Maxwell's second equation:
The equation, which is Gauss's law in magnetism, shows that the surface integral of magnetic field over a
closed surface is zero. This indicates that the totalnumber of magnetic lines of force entering a closed surface
is equal to the total number leavingthe surface. It also predicts that magnetic lines of force form closed
continuous paths; this explains the non-existence of magnetic monopoles.
=ò
 

B dA 0
3.Maxwell's third equation:
The equation, which is Faraday's law of electromagnetic induction, gives the relation between the electric field
and the changing magnetic flux. This law shows that the line integral of electric field around any closed path is
equal to the rate of change of magnetic flux through the surface bounded by the closed path.
F
= -ò

 
B
d
E d
dt
4.Maxwell's fourth equation:
The equation, which is Ampere–Maxwell law, shows that the magnetic field around any closed path is related
to the conduction current and displacement current through that path. Thisequation verifies that magnetic
field can be produced by conduction as well as displacement current.
F
= m e + m Iò

 
E
0 0 0 c
d
B d
dt
On the basis of these four equations, Maxwell predicted the following:
1 .Accelerated charge acts as a source ofelectromagnetic waves.
2. Electromagnetic waves are transverse in nature.
3. Electromagnetic waves propagate through space with a speed of 3 × 10
8
m/s.
4. Light is an electromagnetic wave which travels with a speed of 3 × 10
8
m/s.
A capacitor, made of two parallelplates each of plate area A and separation d, is being charged by an
external ac source. Show that the displacement current inside the capacitor is being charged by an
external ac source. Show that the displacement current inside the capacitor is the sameas current
charging the capacitor? [2/2013]
A capacitor has been charged by a dc source. What are the magnitudes of conduction and
displacementcurrents, when it is fully charged? [1/2012]

7. ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 5
ELECTROMAGNETIC WAVES
Source of electromagnetic waves
As the stationary charge produces an electrostatic field and charge moving with constant velocity
produces magnetic field (also electric field).
In this sequenceMaxwellpointed out that a change in either electric or magnetic field with time producesthe
other field. From this Maxwell concluded that variation of electric and magnetic field vectors perpendicular to
each other leads to the production of electromagnetic disturbances in space. These disturbances show
properties of waves and can travel in space even without any material medium. These waves are called
electromagnetic waves.
Features of electromagnetic waves
(i)The electric and magnetic fieldsE

andB

, respectively, are always perpendicular to the direction in which
the wave is traveling. Thus, the wave is atransverse wave.
(ii)The electric field is always perpendicular to the magnetic field.
(iii)The cross-productE

×B

always gives the direction in which the wave travels.
(iv)The fields always vary sinusoidally, just like the transverse waves. Moreover, the fields vary with the
same frequency andin phasewith each other.
Mathematical form of electromagnetic waves
Consider an electromagnetic wave travelingtoward the positive direction of the x-axis having the electric field
oscillating parallelto the y-axis, and that the magnetic field is oscillating parallel to the z-axis.
Electromagnetic wave
We can write the electric and magnetic fields as sinusoidal functions of position x (along the path of the wave)
and time t:
E = Emsin (kx–wt),
and B = Bmsin (kx–wt),
WhereEmandBmare the amplitudes of the fields andwisangular frequency.Here k is related to the wave
lengthlof the wave by the usual equation.
2
k


=
k is the magnitude of the wave vector (or propagationvector) and its direction describes the direction of
propagation of the wave. The speed of propagation of the wave is (w/k).
w= ck, where,
0 0
1
c=
m e
The relationw= ckis the standard one for waves. This relation is often writtenin terms of frequency,
(=ω/2π) and wavelength,λ(=2π/k) as
2
2 c



= or
λ= c
ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 5
ELECTROMAGNETIC WAVES
Source of electromagnetic waves
As the stationary charge produces an electrostatic field and charge moving with constant velocity
produces magnetic field (also electric field).
In this sequenceMaxwellpointed out that a change in either electric or magnetic field with time producesthe
other field. From this Maxwell concluded that variation of electric and magnetic field vectors perpendicular to
each other leads to the production of electromagnetic disturbances in space. These disturbances show
properties of waves and can travel in space even without any material medium. These waves are called
electromagnetic waves.
Features of electromagnetic waves
(i)The electric and magnetic fieldsE

andB

, respectively, are always perpendicular to the direction in which
the wave is traveling. Thus, the wave is atransverse wave.
(ii)The electric field is always perpendicular to the magnetic field.
(iii)The cross-productE

×B

always gives the direction in which the wave travels.
(iv)The fields always vary sinusoidally, just like the transverse waves. Moreover, the fields vary with the
same frequency andin phasewith each other.
Mathematical form of electromagnetic waves
Consider an electromagnetic wave travelingtoward the positive direction of the x-axis having the electric field
oscillating parallelto the y-axis, and that the magnetic field is oscillating parallel to the z-axis.
Electromagnetic wave
We can write the electric and magnetic fields as sinusoidal functions of position x (along the path of the wave)
and time t:
E = Emsin (kx–wt),
and B = Bmsin (kx–wt),
WhereEmandBmare the amplitudes of the fields andwisangular frequency.Here k is related to the wave
lengthlof the wave by the usual equation.
2
k


=
k is the magnitude of the wave vector (or propagationvector) and its direction describes the direction of
propagation of the wave. The speed of propagation of the wave is (w/k).
w= ck, where,
0 0
1
c=
m e
The relationw= ckis the standard one for waves. This relation is often writtenin terms of frequency,
(=ω/2π) and wavelength,λ(=2π/k) as
2
2 c



= or
λ= c
ELECTROMAGNETIC WAVES
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ELECTROMAGNETIC WAVES
Source of electromagnetic waves
As the stationary charge produces an electrostatic field and charge moving with constant velocity
produces magnetic field (also electric field).
In this sequenceMaxwellpointed out that a change in either electric or magnetic field with time producesthe
other field. From this Maxwell concluded that variation of electric and magnetic field vectors perpendicular to
each other leads to the production of electromagnetic disturbances in space. These disturbances show
properties of waves and can travel in space even without any material medium. These waves are called
electromagnetic waves.
Features of electromagnetic waves
(i)The electric and magnetic fieldsE

andB

, respectively, are always perpendicular to the direction in which
the wave is traveling. Thus, the wave is atransverse wave.
(ii)The electric field is always perpendicular to the magnetic field.
(iii)The cross-productE

×B

always gives the direction in which the wave travels.
(iv)The fields always vary sinusoidally, just like the transverse waves. Moreover, the fields vary with the
same frequency andin phasewith each other.
Mathematical form of electromagnetic waves
Consider an electromagnetic wave travelingtoward the positive direction of the x-axis having the electric field
oscillating parallelto the y-axis, and that the magnetic field is oscillating parallel to the z-axis.
Electromagnetic wave
We can write the electric and magnetic fields as sinusoidal functions of position x (along the path of the wave)
and time t:
E = Emsin (kx–wt),
and B = Bmsin (kx–wt),
WhereEmandBmare the amplitudes of the fields andwisangular frequency.Here k is related to the wave
lengthlof the wave by the usual equation.
2
k


=
k is the magnitude of the wave vector (or propagationvector) and its direction describes the direction of
propagation of the wave. The speed of propagation of the wave is (w/k).
w= ck, where,
0 0
1
c=
m e
The relationw= ckis the standard one for waves. This relation is often writtenin terms of frequency,
(=ω/2π) and wavelength,λ(=2π/k) as
2
2 c



= or
λ= c

8. ELECTROMAGNETIC WAVES
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Electromagnetic wave’s speed (invacuum) is given by the symbol c rather than v. The value of c is
0 0
1
c=
m e
which is about3.0 ×10
8
m/s. We will also see that the wave speed c and the amplitudes of the electric and
magnetic fields are related by
m
m
E
c
B
=(Amplituderatio).
&
E
c
B
= (magnitude ratio).
Medium requirement for EM waves
The wavesrequire a medium (some material) through which or along which to travel. We had waves traveling
along a string, through the Earth, and through the air. However, an electromagnetic wave is curiously different
because it requires no medium for its travel.It can travel through a medium (such as air or glass) as well as
through the vacuum of space between a star and us.
Speed of EM waves
Light has the same speed regardless of the frame of reference from which it is measured.If we send a
beam of light alongan axis and ask several observers to measure its speed while they move at different speeds
alongthat axis, either in the direction of the light or opposite to it, they will all measure the same speed for the
light.
Speed of EM waves as unit of length
The SI unit of length meter is defined as the length of the path traveled by light in vacuumduring a time interval
of (1/299,792,458) of a second. According to this definition of meter,the speed of light (which is an
electromagnetic wave) in vacuum has the exact value
c = 299,792,458 m/s,
which can be used as a standard. In fact, if we now measure the travel time of a pulse of light fromone point to
another, we are not really measuring the speed of the light but rather the distance between those two points.
Energy & momentum carried by EM waves
Electromagnetic waves carry both energy and momentum.In a region of freespace having electric field of
magnitudeE,the energy density will be(eoE
2
/2). Similarly, magneticenergy density associated with a
magnetic field of magnitudeB is (B
2
/2µo). We know that electromagnetic waves contain both electric and
magnetic fields due to which they have a non-zero energy density. If we consider a plane perpendicular to the
direction of propagation of electromagnetic waves, the charges in this plane acquire energy and momentum
from the waves.
(a) An em wave is travelling in a medium with a velocityv vi.=


Draw a sketch showing the propagation
of the em wave, indicating the direction of the oscillating electric and magnetic fields.
(b) How are the magnitudes of the electric and magnetic fields related to the velocity of the em wave?
[2/2012]
What are the direction of electric and magnetic field vectors relative to each other and relative to the
direction of propagation of electromagnetic waves? [1/2012]

9. ELECTROMAGNETIC WAVES
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Radiation Pressure generated by EM waves
The force exerted by an electromagnetic wave on unit area of a surface is calledradiationpressure.
Electromagnetic waves have linear momentum as well as energy. This means that we can exert apressurea
radiation pressureon an object by shining light on it. However, the pressure mustbe very small.
To find an expression for pressure, let usshine a beam of electromagnetic radiation light, forexample on an
object for a timeintervaltD.Further, let us assume that the object is free to moveand that the radiation is
entirelyabsorbed(taken up) by the object. This meansthat during the intervaltD,the object gains energy
UDfrom the radiation. Maxwell showed that the object also gains linear momentum. The magnitudePDof
the momentum change of the object is related to the energy changeUDby
U
p
c
D
D = (Totalabsorption),
Wherec is the speed of light. The direction of the momentum change of the object is the directionof the incident
(incoming) beam that the object absorbs.
Polarization of EM waves
Very high frequency (VHF) television antennas are of two types: (a) vertically oriented and (b) horizontally
oriented. The difference is due to the direction ofoscillation of the electromagnetic waves carrying the TV
signal.In many countries, the transmitting equipment is designed toproduce waves that are polarized
vertically; that is, their electric field oscillates vertically. Thus, forthe electric field ofthe incident television
waves to drive a current along an antenna (and provide a signal to a television set), the antenna must be
vertical. In many other countries, the waves are polarized horizontally.
Figure (a) Figure (b)
Above figure (a) shows an electromagnetic wave with its electric field oscillating parallel to the vertical y-axis.
The plane containing theE

vectoris called theplane of oscillationof the wave (hence, the wave is said to
be plane-polarized in the y-direction). We can represent the wave's polarization (state of being polarized) by
showing the directions of the electric field oscillations ina head-on view of the plane of oscillation,as in Fig.
(b). The vertical double arrow in that figureindicates that as the wave travels past us, its electric field oscillates
vertically–it continuously changes between being directed up and down the y-axis.
ELECTROMAGNETIC WAVES
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AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 7
Radiation Pressure generated by EM waves
The force exerted by an electromagnetic wave on unit area of a surface is calledradiationpressure.
Electromagnetic waves have linear momentum as well as energy. This means that we can exert apressurea
radiation pressureon an object by shining light on it. However, the pressure mustbe very small.
To find an expression for pressure, let usshine a beam of electromagnetic radiation light, forexample on an
object for a timeintervaltD.Further, let us assume that the object is free to moveand that the radiation is
entirelyabsorbed(taken up) by the object. This meansthat during the intervaltD,the object gains energy
UDfrom the radiation. Maxwell showed that the object also gains linear momentum. The magnitudePDof
the momentum change of the object is related to the energy changeUDby
U
p
c
D
D = (Totalabsorption),
Wherec is the speed of light. The direction of the momentum change of the object is the directionof the incident
(incoming) beam that the object absorbs.
Polarization of EM waves
Very high frequency (VHF) television antennas are of two types: (a) vertically oriented and (b) horizontally
oriented. The difference is due to the direction ofoscillation of the electromagnetic waves carrying the TV
signal.In many countries, the transmitting equipment is designed toproduce waves that are polarized
vertically; that is, their electric field oscillates vertically. Thus, forthe electric field ofthe incident television
waves to drive a current along an antenna (and provide a signal to a television set), the antenna must be
vertical. In many other countries, the waves are polarized horizontally.
Figure (a) Figure (b)
Above figure (a) shows an electromagnetic wave with its electric field oscillating parallel to the vertical y-axis.
The plane containing theE

vectoris called theplane of oscillationof the wave (hence, the wave is said to
be plane-polarized in the y-direction). We can represent the wave's polarization (state of being polarized) by
showing the directions of the electric field oscillations ina head-on view of the plane of oscillation,as in Fig.
(b). The vertical double arrow in that figureindicates that as the wave travels past us, its electric field oscillates
vertically–it continuously changes between being directed up and down the y-axis.
ELECTROMAGNETIC WAVES
ELCTRIC CHARGES AND FIELS
AARAV CLASSES 11 C 6, Parijat Colony, Mahaveer Nagar III, Kota (Raj.)Ph.09509469541 7
Radiation Pressure generated by EM waves
The force exerted by an electromagnetic wave on unit area of a surface is calledradiationpressure.
Electromagnetic waves have linear momentum as well as energy. This means that we can exert apressurea
radiation pressureon an object by shining light on it. However, the pressure mustbe very small.
To find an expression for pressure, let usshine a beam of electromagnetic radiation light, forexample on an
object for a timeintervaltD.Further, let us assume that the object is free to moveand that the radiation is
entirelyabsorbed(taken up) by the object. This meansthat during the intervaltD,the object gains energy
UDfrom the radiation. Maxwell showed that the object also gains linear momentum. The magnitudePDof
the momentum change of the object is related to the energy changeUDby
U
p
c
D
D = (Totalabsorption),
Wherec is the speed of light. The direction of the momentum change of the object is the directionof the incident
(incoming) beam that the object absorbs.
Polarization of EM waves
Very high frequency (VHF) television antennas are of two types: (a) vertically oriented and (b) horizontally
oriented. The difference is due to the direction ofoscillation of the electromagnetic waves carrying the TV
signal.In many countries, the transmitting equipment is designed toproduce waves that are polarized
vertically; that is, their electric field oscillates vertically. Thus, forthe electric field ofthe incident television
waves to drive a current along an antenna (and provide a signal to a television set), the antenna must be
vertical. In many other countries, the waves are polarized horizontally.
Figure (a) Figure (b)
Above figure (a) shows an electromagnetic wave with its electric field oscillating parallel to the vertical y-axis.
The plane containing theE

vectoris called theplane of oscillationof the wave (hence, the wave is said to
be plane-polarized in the y-direction). We can represent the wave's polarization (state of being polarized) by
showing the directions of the electric field oscillations ina head-on view of the plane of oscillation,as in Fig.
(b). The vertical double arrow in that figureindicates that as the wave travels past us, its electric field oscillates
vertically–it continuously changes between being directed up and down the y-axis.

10. ELECTROMAGNETIC WAVES
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ELECTROMAGNETIC SPECTRUM
An orderly distribution of electromagnetic waves according to their frequency or wavelength is known
as theelectromagnetic spectrum.
An electromagnetic wave, like any periodic wave, has a frequencynand a wavelengthlthat arerelated to
the speedv of the wave byv =nl. For electromagnetic waves traveling through a vacuumor, to a good
approximation, through air, the speed is v = c, so c =nl.
AsFig. shows, electromagnetic waves exist with an enormous range of frequencies, fromvalues less than 10
4
Hz to greater than 10
24
Hz. Since all these waves travel through a vacuum at thesame speed given by
c = 3 x 10
8
m/s, the equationv =nlcan be used to find the correspondinglywide range of wavelengths. The
ordered series of electromagnetic wave frequencies or wave-lengths is called theelectromagnetic spectrum.
Beginning on the left in Fig. we findradio waves. Lower-frequency radio waves are generally produced by
electrical oscillator circuits, while higher-frequency radio waves (calledmicrowaves) are usually generated
using electron tubes called klystrons.Infrared radiation, some-times loosely called heat waves, originates with
the vibration and rotation of molecules within a material.Visible lightis emitted by hot objects, such as the
Sun, a burning log, or the filament of an incandescent light bulb, when the temperature is high enough to
excite the electrons withinan atom.Ultravioletfrequencies can be produced from the discharge of an electric
arc.X-raysareproduced by the sudden deceleration of high-speed electrons; and, finally,gamma raysare
radiation from nuclear decay.
RADIO WAVES
Electromagnetic waves whose frequency is in the range of 500 kHz to 1000 MHz are known asradio
waves.
Radio waves are produced by the accelerated motion of charged particles in conducting wires. Different
frequency ranges of radio waves are used for different communication systems.For amplitude modulated
(AM) band, the frequency range is 530-1710 kHz. For short wave bandsused in sky wave propagation, the
frequency range is 1710 kHz-54MHz.For television waves thefrequency range is 54-890 MHz. Forfrequency
ELECTROMAGNETIC WAVES
8 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
ELECTROMAGNETIC SPECTRUM
An orderly distribution of electromagnetic waves according to their frequency or wavelength is known
as theelectromagnetic spectrum.
An electromagnetic wave, like any periodic wave, has a frequencynand a wavelengthlthat arerelated to
the speedv of the wave byv =nl. For electromagnetic waves traveling through a vacuumor, to a good
approximation, through air, the speed is v = c, so c =nl.
AsFig. shows, electromagnetic waves exist with an enormous range of frequencies, fromvalues less than 10
4
Hz to greater than 10
24
Hz. Since all these waves travel through a vacuum at thesame speed given by
c = 3 x 10
8
m/s, the equationv =nlcan be used to find the correspondinglywide range of wavelengths. The
ordered series of electromagnetic wave frequencies or wave-lengths is called theelectromagnetic spectrum.
Beginning on the left in Fig. we findradio waves. Lower-frequency radio waves are generally produced by
electrical oscillator circuits, while higher-frequency radio waves (calledmicrowaves) are usually generated
using electron tubes called klystrons.Infrared radiation, some-times loosely called heat waves, originates with
the vibration and rotation of molecules within a material.Visible lightis emitted by hot objects, such as the
Sun, a burning log, or the filament of an incandescent light bulb, when the temperature is high enough to
excite the electrons withinan atom.Ultravioletfrequencies can be produced from the discharge of an electric
arc.X-raysareproduced by the sudden deceleration of high-speed electrons; and, finally,gamma raysare
radiation from nuclear decay.
RADIO WAVES
Electromagnetic waves whose frequency is in the range of 500 kHz to 1000 MHz are known asradio
waves.
Radio waves are produced by the accelerated motion of charged particles in conducting wires. Different
frequency ranges of radio waves are used for different communication systems.For amplitude modulated
(AM) band, the frequency range is 530-1710 kHz. For short wave bandsused in sky wave propagation, the
frequency range is 1710 kHz-54MHz.For television waves thefrequency range is 54-890 MHz. Forfrequency
ELECTROMAGNETIC WAVES
8 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
ELECTROMAGNETIC SPECTRUM
An orderly distribution of electromagnetic waves according to their frequency or wavelength is known
as theelectromagnetic spectrum.
An electromagnetic wave, like any periodic wave, has a frequencynand a wavelengthlthat arerelated to
the speedv of the wave byv =nl. For electromagnetic waves traveling through a vacuumor, to a good
approximation, through air, the speed is v = c, so c =nl.
AsFig. shows, electromagnetic waves exist with an enormous range of frequencies, fromvalues less than 10
4
Hz to greater than 10
24
Hz. Since all these waves travel through a vacuum at thesame speed given by
c = 3 x 10
8
m/s, the equationv =nlcan be used to find the correspondinglywide range of wavelengths. The
ordered series of electromagnetic wave frequencies or wave-lengths is called theelectromagnetic spectrum.
Beginning on the left in Fig. we findradio waves. Lower-frequency radio waves are generally produced by
electrical oscillator circuits, while higher-frequency radio waves (calledmicrowaves) are usually generated
using electron tubes called klystrons.Infrared radiation, some-times loosely called heat waves, originates with
the vibration and rotation of molecules within a material.Visible lightis emitted by hot objects, such as the
Sun, a burning log, or the filament of an incandescent light bulb, when the temperature is high enough to
excite the electrons withinan atom.Ultravioletfrequencies can be produced from the discharge of an electric
arc.X-raysareproduced by the sudden deceleration of high-speed electrons; and, finally,gamma raysare
radiation from nuclear decay.
RADIO WAVES
Electromagnetic waves whose frequency is in the range of 500 kHz to 1000 MHz are known asradio
waves.
Radio waves are produced by the accelerated motion of charged particles in conducting wires. Different
frequency ranges of radio waves are used for different communication systems.For amplitude modulated
(AM) band, the frequency range is 530-1710 kHz. For short wave bandsused in sky wave propagation, the
frequency range is 1710 kHz-54MHz.For television waves thefrequency range is 54-890 MHz. Forfrequency

11. ELECTROMAGNETIC WAVES
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modulated (FM) band, which is used for commercialFM radio the frequency range is 88-108 MHz. For cellular
phones, the frequency range is 300-3000MHz [ultra high frequency band (UHF)].
Uses of Radio Wave
Radio waves are used in communication systems such as
(i)Radio,
(ii)Television, and
(iii)Cellular phones.
MICROWAVES
The shortest wavelength radio waves are calledmicrowaves,because even though their wave-lengths are
much longer than those of visiblelight, they are orders of magnitude smaller than the wavelengths used for
radio broadcasting. Microwaves are produced by special vacuum tubes, namely, klystrons, magnetrons, and
Gunn diodes. Microwave ovens are an interesting domestic application of microwaves. They are generally
used to warm or cook food. All food items such as vegetables, fruits, etc. contain water molecules. The
frequency of microwaves in the oven is selected according to the resonant frequency of water molecules so
that the energy of the micro-waves increases the kinetic energy of water molecules. This increases the
frequency of random motion of the water molecules. These water molecules share this energy with
neighboring food molecules, heating up the food.
Uses of microwaves Wave
(i)Microwaves are used in radar systems for aircraft navigation.
(ii)They are used in microwave ovens for cooking food.
(iii)A radar using microwaves can be used to detect speed of a tennis ball, cricket ball, or automobilesin
motion.
INFRARED WAVES
Electromagneticwaves having frequency range3 × 10
11
–4 × 10
14
Hz are known asinfraredwaves.
All hot bodies radiate infrared waves. Since infrared waves do not lie in the visible spectrum,they cannot be
viewed by naked eyes. These waves are also known as heat wavesbecause water,carbon dioxide, and
ammonia molecules present in majority of substances readily absorb infra-red waves, due to which the
thermal motion of these molecules increases and heat up their surroundings.
Uses ofinfraredWave
(i)In infrared lampswhich are used for physical therapy.
(ii)In infrared detectors used in Earth satellites.
(iii)In light-emitting diodes which emit infrared waves and are used in remote switches of TV, CD player,
and air conditioners.
(iv)In solar water heaters and solar cookers.
(v)Ingreen houses which work on basis of greenhouse effect to maintain constant temperature inside the
green house, that is adequate for a plant to grow properly.
(vi)In maintaining Earth's warmth through the greenhouse effect. The sunlight (or visible light) whicheasily
crosses the atmospheric layer is absorbed by the Earth's surface and radiated asinfrared radiation.
These infrared radiations are trapped by gases such as CO2and water vaporwhich are also known as
greenhousegases. The trapped infraredradiations are responsible forthe average temperature of the
Earth.
How are radio waves produced? [1/2011]
To which part of the electromagnetic spectrum does a wave of frequency 3 × 10
13
Hz belong? [1/2014]

12. ELECTROMAGNETIC WAVES
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VISIBLE RAYS
Electromagnetic waves that are visible to the human eye are known as visible rays.They have a
wavelength ranging from 400 to 700 nm and a frequency range of 4 × 10
14
Hz toabout7 × 10
14
Hz.
Visible rays emitted and reflected from objects around us enableus to see the various objects inthe
surroundings. When visible rays emitted by a light source such as a bulb or a tube light strikean object, they
scatter in all directions. A few of the visible rays reflect back toward the eye of theobserver due to which we are
able to see the object.Our eyes are sensitive to this range of wavelengths. Different animals are sensitive to
different range of wavelengths. For example, snakes can detect infrared waves, and the ‘visible’ range of
many insects extends well into the ultraviolet.
Uses of Visible Rays
(i)In electric bulbs and tube lights.
(ii)In lasers.
(iii)In movie screen in a cinema hall.
ULTRAVIOLET RAYS
Electromagnetic waves which have wavelength in the range 0.6-400 nm and frequency in the range of
8 × 10
14
Hz to 5 × 10
16
Hz are known asultraviolet rays.
Ultraviolet rays (or UV rays) are produced by special lamps and also by very hot bodies such as theSun.
Ultraviolet rays are of high frequency or short wavelength, and are therefore of high energy. Exposure to
ultraviolet radiation in large quantities has harmful effects on humans. For example,exposure to UV radiation
can cause tanning of skin due toproduction of more melanin. Since glassabsorbs UV radiation, therefore one
cannot get tanned or sunburn through a glass window. Due tothis special property of glass, welders wear
special glass goggles or face masks with glass windowsto protect their eyes from exposure to large amount of
UV radiation produced during welding.
Ultraviolet radiation can be focused into very narrow beams due to their short wavelength, for high-precision
applications such as LASIK (Laser-assisted in situ keratomileusis) eye surgery. Sun emits ultraviolet rays
along with visible and infrared rays but majority of ultraviolet rays emitted by the Sun are absorbed by the
ozone layer present at an altitude of 40 km to 50 km from the surface of Earth. Thus, ozone layer plays a
protective role in absorbing harmful ultraviolet raysfrom the Sun and so depletion of ozone by
chlorofluorocarbons (CFCs) such as freons is a matterof international concern.
Uses of Ultraviolet Rays
(i)For sterilizing surgical instruments.
(ii)To kill germs inwater purifiers.
(iii)In LASIK eye surgery.
(iv)For checking mineral samples due to their property of causing fluorescence.
(v)In burglar alarms.
X-RAYS
The electromagnetic waves lying beyond the ultraviolet region of electromagnetic spectrum and
having wavelength in the range of 10
-4
nm to 10 nm are known asX-rays.
X-rayscan be produced by bombarding a metal target by high-energy electrons. Care must be taken to avoid
unnecessary or over-exposure to X-rays, because, being high-energy radiations they can destroy living
tissues and organisms.
Welders wear special goggles or face masks with glass windows to protect their eyes from
electromagnetic radiation. Name the radiations and write the range of their frequency.[1/2013]

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Uses of X-Rays
(i)For detectionof fractures in bones.
(ii)By engineers for detecting faults, cracks, holes, and flaws in metals.
(iii)For investigation of crystal structure.
(iv)To detect foreign bodies like diseased organs, stones, and bullets in the human body.
GAMMARAYS
The electromagnetic waves which have wavelength in the range 10
-14
m to 10
-10
m and frequency range
of 3 × 10
18
Hz to 5 × 10
22
Hz are known asgamma rays.
Gamma rays are produced during nuclear reactions and are also emitted by radioactive nuclei. Gamma rays
are high-energyradiations because of their extremely short wavelength (high frequency).
Uses of Gamma Rays
(i)In cancer therapy to destroy cancer cells.
(ii)To preserve food items for long time by exposing them to gamma rays which kill harmful micro
organisms.
(iii)To studystructure of atomic nucleus.
To which part of the electromagnetic spectrum does a wave of frequency 5 × 10
19
Hz belong?[1/2014]

14. ELECTROMAGNETIC WAVES
12 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
Exercise # 1
VSAT
Introductionto electromagnetic waves, ampere–Maxwell law, displacement current,
and Maxwell’s equations
1.What are electromagnetic waves?
2.What oscillates in electromagnetic waves? Are these waves transverse orlongitudinal?
3.Write the formula for velocity of electromagnetic waves in free space.
4.What is displacement current? Write its unit.
5.Are conduction and displacement currents same?If not then write difference between them.
6.A variable frequency source is connected to a capacitor. Will the displacement current increaseor decrease
with increasein frequency?
7.Does electromagnetic wave exert some force on the surface on which it is incident?
Electromagnetic waves, travelingelectromagnetic waves, and electromagnetic spectrum
8.Arrange the given electromagnetic radiations in the descending order of their frequencies:Infrared, X-rays,
ultra-violet rays, andg-rays.
9.What is the name given to that part of electromagnetic spectrumwhich is used in radarsystem?
10.Why are microwaves used in radar?
11.Name the electromagnetic radiation used for viewing objects through haze and fog.
12.Which part of the electromagnetic spectrum has the largest penetrating power?
13.How are electric and magnetic field vectors related to each other in case of electromagnetic wave?
14.If a charge is oscillating with frequency of 100 Hz, what will be the wavelength of electromagnetic wave
radiated by it?
SAT
introduction to electromagnetic waves, ampere–Maxwell law, displacement current,
and Maxwell’s equations
1.An electromagnetic radiation has energy 11 KeV. To which region of electromagnetic spectrum does it belong
to? Give any two uses of this radiation.
2.How can the electric portion of theelectromagnetic wave be detected?
3.The charging current for a capacitor is 0.25 A. What is the displacement current across its plates?
4.Show that the average energy density of the electricfield equals theaverage energy density of the magnetic
field.
5.Why shortwave communication over long distances is not possible via ground waves?
Electromagnetic waves, traveling electromagnetic waves, and electromagnetic spectrum
6.To which part of the electromagnetic spectrum do the following belong:
(a) () () ()l = u l = l =
0
9
0.2m, b =10 Hz, c 0.2mm, and d 5890A .
7.How do we make television broadcasts for larger coverage and for long distance?

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8.Scientists put X-ray astronomical telescope on the artificial satelliteorbiting above the Earth’s atmosphere
whereas theybuildoptical and radio-telescopes on the surface of the Earth. Why?
9.For an electromagnetic wave, write the relationship between amplitude of electric and magnetic fields in free
space.
10.Name the part of electromagnetic spectrum to which waves of wavelength (a)1 A
0
and (b) 10
-2
m belong-.
Using the relation( )T 0.29cml = K, obtain the characteristic Kelvin temperature corresponding to these two
wavelengths.
LAT
Introduction to electromagnetic waves, ampere–Maxwell law, displacement current,
andMaxwell’s equations
1.A certain helium-neon laser emits red light in a narrow band of wavelengths centered at 632.8 nm andwith a
“wavelength width”of 0.0100 nm. What is thecorresponding “frequency width” for the emission?
Electromagnetic waves, travelingelectromagnetic waves, and electromagnetic spectrum
2.Electromagnetic waves with wavelength (a)
1
lare used to treat muscular strain, (b)
2
lare used by a FM radio
station forbroadcasting, (c)
3
lare used to detect fracture in bones, and (d)
4
lare absorbed by the ozone
layer of the atmosphere.Identify and name thepart of the electromagnetic spectrum to which theseradiation
belong. Arrangethese wavelengthsin decreasing order of magnitude.
3.Electromagnetic waves travel in a medium with a speed of 2 x 10
8
m/s. The relative permeability of the
medium is 1. Find the relative permittivity.
4.(a) Prove that electromagnetic waves are transverse in nature. (b) Deduce therelation
0 0
c 1/= m e
Electromagnetic waves of frequency 5 x 10
14
Hz are passed through a liquid. The wavelength of the waves in
liquid is measured to be 4.5 x 10
-7
m. Calculate (a) the wavelength of electromagnetic wave in vacuum, (b)
velocity of electromagnetic waves in the liquid, and (c) refractive index of the liquid. Given, velocity of
electromagnetic waves in vacuum = 3 x 10
8
m/s.

16. ELECTROMAGNETIC WAVES
14 11 C 6, ParijatColony, MahaveerNagarIII,Kota(Raj.)Ph.09509469541 AARAV CLASSES
Exercise#2
1.Arrange the given electromagnetic radiation in the descending order of their frequencies:Infra-red, X-rays,
Ultraviolet and Gamma rays. [2002]
2.Write any twoapplicationsof X-rays. [2003]
3.What is the name given tothat partof electromagnetic spectrum which is used for taking photographs of earth
under foggy conditions from great heights? [2004]
4.Write any four characteristics of electromagnetic waves. Give two uses each of (i) Radio-waves. (ii) Micro-
waves. [2007]
5.Name the part of the electromagnetic spectrum of wavelength10
-2
m and mention its one application.[2007]
6.The oscillating magnetic field in a plane electromagnetic wave is given by
()
6 11
y
B 8 x 10 sin 2 x 10 t 300 x T
-
é ù= + p
ë û
(i)Calculate thewavelength of the electromagnetic wave.
(ii)Write down the expression for the oscillating electric field. [2008]
7.Write the following radiation in ascending order inrespect of their frequencies: X-rays, microwaves, UV rays
and radio waves. [2009]
8.How does a charge q oscillating at certain frequency produce electromagnetic waves? Sketch a schematic
diagram depicting electric and magnetic fields for an electromagnetic wave propagating along the Z-direction.
[2009]
9.Which part of electromagnetic spectrum has largest penetrating power? [2010]

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Ashok Saini
(SMC, Sagar)
Mohd.Khali dKhan
(GM Collage, Betiah)
Ankur Kumar
(NMCH Patna)
Aliya Naz
(MGM, Jamshedpur)
Anushka Tyagi
(DSIKL, Banglore)
Rameshwer Shinde
(BIMC, Pune)
Rahul Kirade
(GMC, Indore)
Vishal Shrivastav
(BRD, Gorakhpur)