Download Electric field

Electromagnetic Radiation
Electromagnetic spectrum
“Let there be electricity an magnetism
and there is light”
J.C. Maxwell
Maxwell’s equations are independent of wavelength
For stationary charges
1
the electric force field 
2
r
Coulomb’s law
© 2005 Pearson Prentice Hall, Inc
© 2005 Pearson Prentice Hall, Inc
© 2005 Pearson Prentice Hall, Inc
If a charge moves nonuniformly, it radiates
The electric field of a moving point charge
http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html
Electric field
q
E t  
4 0
 er  r  d  er   1 d

 r 2  c dt  r 2   c 2 dt 2 er  
 


2
er  :unit vector directed from q to P at earlier time
q
-
P
r
The retarded time/ the time delay 
c
The retarded distance = r
Law of radiation
q
2
d er 
E
2
2
4 0 c dt
Magnetic field
B  er   E c
Electric field produced by a slowly moving charge q at a distance r
P
a'
 r
E (t )  
a  t   sin 
2
4 0c r  c 
q
q
©SB/SPK
Sinusoidal Oscillation
P
©SB/SPK
Electric field
E (t )  
q
a (t  r / c)sin
4 0 c r
2
qy0
E (t ) 
cos[ (t  r / c)]sin
2
4 0 c r
2
Electric field along x axis
qy0

  
E ( x, t ) 
cos

t

x




2
4 0 c x
c 

2
Electric field at a large distance
 

E y ( x ,t )  E0 cos t  x 
c 

 E0 cos( t  kx )
Magnetic field
eˆr  iˆ

E  E y  x, t  ˆj


B x, t   iˆ  E  x, t  c
E
 cost  kx k̂
c
ELECTROMAGNETIC WAVE is a TRANSVERSE WAVE
 E
 E   0 0 2
t
2
 B
2
 B   0 0 2
t
2
2
0 : permitivity of free space
0: permeability of free space
Maxwell’s wave equation in free space
Dipole moment
Charge q oscillating as y(t) produces the
same electric field as q/2 moving as y(t)
and –q/2 moving as –y(t)
The latter is an oscillating dipole
d y ( t )  qy( t )  d 0 cos( t )
q
d 0   2 y0
2
Electric field in terms of dipole moment
qy0
E (t ) 
cos[

(
t

r
/
c
)]sin

2
4 0c r
2
E( t )  
1
4 0 c r
2
dy ( t  r / c ) sin 
Current
I (t )  q (t )
d y  lI (t )
I (t )   Isin(t )
Electric field in terms of current
lI
E (t ) 
cos[ (t  r / c)]sin 
2
4 0 c r
Electric field at a distance r at time t
qy0

  
E (t ) 
cos t    r  sin 
2
4 0 c r
c 

2
lI

  
E (t ) 
cos t    r  sin 
2
4 0 c r
c 

Energy Density: Energy per unit volume
1
1 2
2
U  0E 
B
2
2 0
1
1
2
2
U  0E  2 E
2
2c  0
U  0E
2
c 
2
1
 0 0
Average Energy Density
E  x, t   E cos(t  kx)
E
2
 E /2
2
1
2
U  0E
2
Energy Flux Density: Energy per unit area
per unit time
 q y   sin 
S  U c
 2 rˆ
 32 c  0  r
2
2 4
0
2 3
2
Power radiated per unit solid angle
Radiation pattern of electric dipole
Electric Dipole Oscillator
© SPK/SB
Dipole radiation
© SPK/SB
© SPK/SB
TV Antenna
Car Antenna
Ooty Radio Telescope
0.5 m
530 m long 30 m wide parabolic cylinder
1054 dipoles, 326.5 MHz
© SB
0.5 m
© SB
The Radio Milky Way
The image shows the Milky Way galaxy
as it would appear if we could see the
electromagnetic energy the hydrogen in
the galaxy emits in the Radio region,
specifically the 21-cm wavelength. This
image is computer generated from data
collected by various radio telescopes.
© NRAO Green Bank
Microwave background fluctuation
cosmic microwave background fluctuations are extremely faint. The
cosmic microwave background radiation is a remnant of the Big Bang
and the fluctuations are the imprint of density contrast in the early
universe.
Ultraviolet Galaxy
NGC 1365
©NASA/JPL-Caltech/SSC
Accelerating charge gives rise to radiation
Sinusoidal motion of charge gives rise to electromagnetic
radiation gives rise to plane electromagnetic wave at a
large distance.
The direction of electric field, magnetic field and propagation
are mutually perpendicular to each other.
Electric and magnetic field are in phase.
1. FEYNMAN LECTURES ON PHYSICS VOL I
Author : RICHARD P FEYNMAN,
IIT KGP Central Library
Class no. 530.4
2. OPTICS
Author: EUGENE HECHT
IIT KGP Central Library
Class no. 535/Hec/O
Images from Astra's Stellar Cartography Demo