Jgkjfk

1. ELECTROMAGNETIC WAVES
• Types of electromagnetic waves
• Electromagnetic spectrum
• Propagation of electromagnetic wave
• Electric field and magnetic field
• Qualitative treatment of electromagnetic waves

2. • Electromagnetic (EM) waves were first postulated by James Clerk
Maxwell and subsequently confirmed by Heinrich Hertz
• Maxwell derived a wave form of the electric and magnetic equations,
revealing the wave-like nature of electric and magnetic fields, and
their symmetry
• Because the speed of EM waves predicted by the wave equation
coincided with the measured speed of light, Maxwell concluded
that light itself is an EM wave
• According to Maxwell’s equations, a spatially-varying electric
field generates a time-varying magnetic field and vice versa
• Therefore, as an oscillating electric field generates an oscillating
magnetic field, the magnetic field in turn generates an oscillating
electric field, and so on
• These oscillating fields together form an electromagnetic wave
Introduction

3. • In the studies of electricity and magnetism, experimental
physicists had determined two physical constants - the electric
(o) and magnetic (o) constant in vacuum
• These two constants appeared in the EM wave equations, and
Maxwell was able to calculate the velocity of the wave (i.e. the
speed of light) in terms of the two constants:
• Therefore the three experimental constants, o, o and c
previously thought to be independent are now related in a fixed
and determined way
Speed of EM waves
1 8
o o
c   3.0 10 m/s  = 8.8542  10-12 C2 s2/kgm3 (permittivity of vacuum)
0
0 = 4  10-7 kgm/A2s2 (permeability of vacuum)

4. (1) Gauss’s law for the electric field
Gauss’s law is a consequence of the inverse-square nature of Coulomb’s
law for the electrical force interaction between point like charges
(2) Gauss’s law for the magnetic field
This statement about the non existence of magnetic monopole; magnets are
dipolar. Magnetic field lines form closed contours
(3) Faraday’s law of electromagnetic induction
This is a statement about how charges in magnetic flux produce
(non-conservative) electric fields
(4) The Ampere-Maxwell law
This law is a statement that magnetic fields are caused by electric conduction
currents and or by a changing electric flux (via the displacement current)
Maxwell’s Equations

5. 
0

  E 
B

 E  
t
 B  0
E
t
 
 B  0 J  00

Q(V)
0
V
 
E dA 
t
S
B,S
 
E  dl  
V

B dA  0
t
S
E,S
 
Bdl  0 IS  00
Maxwell’s Equations
Formulation in terms of total charge and current
Differential form Integral form
Gauss's law
Gauss's law for
magnetism
Maxwell–Faraday equation
(Faraday's law of induction)
Ampère's circuital law
(with Maxwell's correction)

6. Maxwell’s Equations

S
E dl
line integral of the electric field along the
boundary ∂S of a surface S (∂S is always a
closed curve)

S
B dl
line integral of the magnetic field over the
closed boundary ∂S of the surface S

V
E dA
The electric flux (surface integral of the
electric field) through the (closed)
surface (the boundary of the volume V )

V
B dA
The magnetic flux (surface integral of the
magnetic B-field) through the (closed)
surface (the boundary of the volume V )

7. Electromagnetic Spectrum

8. Generating an Electromagnetic Waves
An arrangement for generating a traveling electromagnetic
wave in the shortwave radio region of the spectrum: an LC
oscillator produces a sinusoidal current in the antenna, which
generate the wave. P is a distant point at which a detector can
monitor the wave traveling past it

9. Generating an Electromagnetic Waves
Variation in the electric field E and the
magnetic field B at the distant point P as
one wavelength of the electromagnetic
wave travels past it.
The wave is traveling directly out of the
page
The two fields vary sinusoidally in
magnitude and direction
The electric and magnetic fields are always
perpendicular to each other and to the
direction of travel of the wave

10. • Close switch and current flows briefly. Sets up electric field
• Current flow sets up magnetic field as little circles around the wires
• Fields not instantaneous, but form in time
• Energy is stored in fields and cannot move infinitely fast
Generating an Electromagnetic Waves

11. • Figure (a) shows first half cycle
• When current reverses in Figure (b), the fields reverse
• See the first disturbance moving outward
• These are the electromagnetic waves
Generating an Electromagnetic Waves

12. • Notice that the electric and
magnetic fields are at right
angles to one another
• They are also perpendicular
to the direction of motion of
the wave
Generating an Electromagnetic Waves

13. Electromagnetic Waves
•
E0 = amplitude of the electric field
B0 = amplitude of the magnetic field
 = angular frequency of the wave
k = angular wave number of the wave
At any specified time and place: E/B = c
E0 /B0 c
(speed of electromagnetic wave)
The cross product EB always gives the direction of travel
of the wave
• Assume that the EM wave is traveling toward P in the positive
direction of an x-axis, that the electric field is oscillating parallel
to the y-axis, and that the magnetic filed is the oscillating
parallel to the z-axis:
E  E0 sin(kxt)
B  B0 sin(kxt)

14. indicates the Poynting vector at that point
Energy Transport and the Poynting VectoS
r
• Like any form of wave, an EM wave can transport from one location to
another, e.g. light from a bulb and radiant heat from a fire
• The energy flow in an EM is measured in terms of the rate of energy flow
per unit area
• The magnitude and direction of the energy flow is described
in terms of a vector called the Poynting vector: S
0
 1  
S 

E B
E, B refer to the fields of a wave at a particular point in space and S
S is perpendicular to the plane formed
by E and B , the direction is determined
by the right-hand rule.