Important Formulas: Electromagnetic Waves

# 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
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
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
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
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
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
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
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
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
scale
circular
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
scale
vernier
scale
main
calliper vernier of ading Re object of Thicknes
Least count of vernier calliper = 1 MSD –1 VSD
```

## Physics for JEE Main & Advanced

289 videos|635 docs|179 tests

## Physics for JEE Main & Advanced

289 videos|635 docs|179 tests

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