Important Electromagnetic Waves Formulas for JEE and NEET

 Page 1


 
ELECTRO MAGNETIC WAVES
Maxwell's equations
?
? ? ?
0
/ Q dA E
(Gauss's Law for electricity)
?
? ? 0 dA B
(Gauss's Law for magnetism)
?
?
? ?
dt
d –
d E
B
? (Faraday's Law)
dt
d
i d B
E
0 0 c 0
?
? ? ? ? ? ?
?
? (Ampere-Maxwell Law)
Oscillating electric and magnetic fields
E= E
x
(t) = E
0
 sin (kz - ?t)
= E
0
 sin ?
?
?
?
?
?
?
?
?
?
?
?
?
? vt –
z
2
= E
0
 sin ?
?
?
?
?
?
?
?
?
?
?
?
?
?
T
t
–
z
2
E
0
/B
0
 = c
c = 0 0
/ 1 ? ?
c is speed of light in vaccum
? ? ? / 1 v
v is speed of light in medium
Page 2


 
ELECTRO MAGNETIC WAVES
Maxwell's equations
?
? ? ?
0
/ Q dA E
(Gauss's Law for electricity)
?
? ? 0 dA B
(Gauss's Law for magnetism)
?
?
? ?
dt
d –
d E
B
? (Faraday's Law)
dt
d
i d B
E
0 0 c 0
?
? ? ? ? ? ?
?
? (Ampere-Maxwell Law)
Oscillating electric and magnetic fields
E= E
x
(t) = E
0
 sin (kz - ?t)
= E
0
 sin ?
?
?
?
?
?
?
?
?
?
?
?
?
? vt –
z
2
= E
0
 sin ?
?
?
?
?
?
?
?
?
?
?
?
?
?
T
t
–
z
2
E
0
/B
0
 = c
c = 0 0
/ 1 ? ?
c is speed of light in vaccum
? ? ? / 1 v
v is speed of light in medium
c
U
p ? 
energy transferred to a surface in time t is U, the magnitude of
the total momentum delivered to this surface (for complete
absorption) is p
Electromagnetic spectrum
Type Wavelength 
range 
Production Detection 
Radio > 0.1m Rapid acceleration and 
decelerations of electrons in 
aerials 
Receiver's aerials 
Microwave 0.1m to 1mm Klystron value or magnetron 
value 
Point contact diodes 
Infra-red 1mm to 700nm Vibration of atoms and 
molecules 
Thermopiles Bolometer, 
Infrared photographic 
film 
Light 700nm to 
400nm 
Electrons in atoms emit light 
when they move from one 
energy level to a lower 
energy 
The eye, photocells, 
Photographic film 
Ultraviolet 400nm to 1nm Inner shell electrons in 
atoms moving from one 
energy level to a lower level 
photocells photographic 
film 
X-rays 1nm to 10
–3
 nm X-ray tubes or inner shell 
electrons 
Photograpic film, Geiger 
tubes, lonisation chamber 
Gamma 
rays 
< 10
–3
nm Radioactive decay of the 
nucleus 
do 
ERROR AND MEASUREMENT
1. Least Count
 
 
mm.scale 
L.C =1mm
Vernier 
L.C=0.1mm
Screw gauge 
L.C=0.1mm 
Stop Watch 
L.C=0.1Sec 
Temp thermometer
L.C=0.1°C 
2. Significant Figures
? Non-zero digits are significant
? Zeros occurring between two non-zeros digits are significant.
? Change of units cannot change S.F.
? In the number less than one, all zeros after decimal point and to
the left of first non-zero digit are insignificant
? The terminal or trailing zeros in a number without a decimal
point are not significant.
Page 3


 
ELECTRO MAGNETIC WAVES
Maxwell's equations
?
? ? ?
0
/ Q dA E
(Gauss's Law for electricity)
?
? ? 0 dA B
(Gauss's Law for magnetism)
?
?
? ?
dt
d –
d E
B
? (Faraday's Law)
dt
d
i d B
E
0 0 c 0
?
? ? ? ? ? ?
?
? (Ampere-Maxwell Law)
Oscillating electric and magnetic fields
E= E
x
(t) = E
0
 sin (kz - ?t)
= E
0
 sin ?
?
?
?
?
?
?
?
?
?
?
?
?
? vt –
z
2
= E
0
 sin ?
?
?
?
?
?
?
?
?
?
?
?
?
?
T
t
–
z
2
E
0
/B
0
 = c
c = 0 0
/ 1 ? ?
c is speed of light in vaccum
? ? ? / 1 v
v is speed of light in medium
c
U
p ? 
energy transferred to a surface in time t is U, the magnitude of
the total momentum delivered to this surface (for complete
absorption) is p
Electromagnetic spectrum
Type Wavelength 
range 
Production Detection 
Radio > 0.1m Rapid acceleration and 
decelerations of electrons in 
aerials 
Receiver's aerials 
Microwave 0.1m to 1mm Klystron value or magnetron 
value 
Point contact diodes 
Infra-red 1mm to 700nm Vibration of atoms and 
molecules 
Thermopiles Bolometer, 
Infrared photographic 
film 
Light 700nm to 
400nm 
Electrons in atoms emit light 
when they move from one 
energy level to a lower 
energy 
The eye, photocells, 
Photographic film 
Ultraviolet 400nm to 1nm Inner shell electrons in 
atoms moving from one 
energy level to a lower level 
photocells photographic 
film 
X-rays 1nm to 10
–3
 nm X-ray tubes or inner shell 
electrons 
Photograpic film, Geiger 
tubes, lonisation chamber 
Gamma 
rays 
< 10
–3
nm Radioactive decay of the 
nucleus 
do 
ERROR AND MEASUREMENT
1. Least Count
 
 
mm.scale 
L.C =1mm
Vernier 
L.C=0.1mm
Screw gauge 
L.C=0.1mm 
Stop Watch 
L.C=0.1Sec 
Temp thermometer
L.C=0.1°C 
2. Significant Figures
? Non-zero digits are significant
? Zeros occurring between two non-zeros digits are significant.
? Change of units cannot change S.F.
? In the number less than one, all zeros after decimal point and to
the left of first non-zero digit are insignificant
? The terminal or trailing zeros in a number without a decimal
point are not significant.
3. Permissible Error
? Max permissible error in a measured quantity = least count of
the measuring instrument and if nothing is given about least count
then Max permissible error = place value of the last number
? f (x,y) = x + y     then   ( ?f)
max
 = max of ( ? ?X ? ?Y)
? ?f (x,y,z) = (constant) x
a
 y
b
 z
c
  then
max
f
f
?
?
?
?
?
? ?
= max of  ?
?
?
?
?
?
?
? ?
?
?
?
?
?
z
z
c
y
y
b
x
x
a
4. Errors in averaging
? Absolute Error   ?a
n
 = |a
mean
 -a
n
|
? Mean Absolute Error ?a
mean
 =   
n
| a |
n
1 i
i
?
?
?
?
?
?
?
?
?
?
?
? Relative error =  
mean
mean
a
a ?
? Percentage error = 
mean
mean
a
a ?
×100
5. Experiments
? Reading of screw gauge
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
circular
reading
scale
main
gauge screw of ading Re object of Thicknes
 least count of screw gauge =
division scale circular of . No
pitch
? Vernier callipers
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
vernier
reading
scale
main
calliper vernier of ading Re object of Thicknes
Least count of vernier calliper = 1 MSD –1 VSD