12 08 Electromagnetic Waves
12 08 Electromagnetic Waves
12 08 Electromagnetic Waves
d∅E
B. dl = μ˳ IC + Ɛ˳
dt
d
B. dl = μ˳ IC + Ɛ˳ E. dA
dt
Displacement current is the current which arises due to time rate of change of
electric flux(∅𝐄 ) in some part of the electric circuit
d∅E
iD = Ɛ˳
dt
⟹When a capacitor is charged or a charge capacitor is allowed to discharge, the
electric flux between the plate of the capacitor change with time it gives rise to
displacement current between the plate
⟹ Displacement current has the same units as electric current, and it is a source of
the magnetic field just as actual current is
⟹The displacement current is precisely equal to the conduction current, when the
two are present in different parts of the circuit
(i) Gauss law in electrostatics. It states that the total electric flux through any closed
surface is always equal to 1 Ɛ˳times the net charge enclosed by the surface
𝐪
𝐄. 𝐝𝐬 = ˳
Ɛ
(ii) Gauss law in magnetism. It states that the net magnetic flux crossing any closed
surface is always zero
𝐁. 𝐝𝐬 = 𝟎
⟹A direct consequence of Gauss' law in magnetism is that an isolated magnetic
monopole does not exist.
(iii) Faraday ‘s law of electromagnetic induction. It states that the induced e.m.f.
produced in a circuit is numerically equal to time rate of change of magnetic flux
through it
d∅B
e=−
dt
⟹ Since e.m.f. can be defined as the line integral of electric field, the above relation
may be expressed as..
𝐝∅𝐁
𝐄. 𝐝𝐥 = −
𝐝𝐭
(iv) Maxwell – Ampere ‘ circuital law . It states that the line integral of magnetic
field along a closed path is equal to 𝛍˳ times the total current sum of conduction(𝐈𝐂 )
and displacement currents(𝐈𝐃 ) threading the surface bounded by that closed path.
𝐝∅𝐄
𝐁. 𝐝𝐥 = 𝛍˳ 𝐈𝐂 + Ɛ˳
𝐝𝐭
ELECTROMAGNETIC WAVES -:
Maxwell gave the idea of electromagnetic waves, while Hertz and other scientists
produced and studied these waves experimentally.
𝐄 = 𝐄˳𝐬𝐢𝐧 𝛚𝐭 − 𝐊𝐱 𝐁 = 𝐁˳𝐬𝐢𝐧 𝛚𝐭 − 𝐊𝐱
2π 2π
ω= K=
T λ
1 γλ=C
γ=
T
γ = Frequency λ = wavelength
T = Time period C = Speed of light
𝐄˳ =Amplitude of electric field
𝐁˳= Amplitude of Magnetic field
Negative sign between t and x implies that wave is
travelling in positive x-axis
(i) Electromagnetic waves propagate in the form of varying electric and magnetic
fields, such that the two fields are perpendicular to each other
(ii) Electromagnetic waves are produced by accelerated charges
(iii) Electromagnetic waves do not require any material medium for their
propagation.
(iv) In free space, electromagnetic waves travel with a velocity(𝐂)
𝟏
𝐂= = 𝟑 𝐗 𝟏𝟎𝟖 𝐦/𝐬
𝛍˳𝛆˳
(v) When an electromagnetic wave travels from one medium to another, its
wavelength changes but frequency remains unchanged.
(vi) The ratio of the amplitude of electric(𝐄˳)& magnetic field(𝐁˳) is constant & it is
equal to velocity of the electromagnetic wave(𝐂)
𝐄˳ 𝐄
=𝐂 𝐨𝐫 =𝐂
𝐁˳ 𝐁
(vi) Energy in electromagnetic wave is divided equally between electric & magnetic
field Vector
(vii) Electromagnetic wave shows interference & diffraction
(viii) Electromagnetic waves are transverse in nature
2
1 2
1 BRMS
Energy UE = ε˳ERMS UB =
UED = UEnergy density = 2 2 μ˳
Volume
E˳ B˳
𝟐
𝐁𝐑𝐌𝐒 ERMS = BRMS =
𝐔𝐄𝐃 = 𝐔𝐄 + 𝐔𝐁 = 𝟐
𝛆˳𝐄𝐑𝐌𝐒 = 2 2
𝛍
UE = UB
U UED C∆t A
I= = = UED C
A∆t A∆t
𝟐
𝟐
𝐁𝐑𝐌𝐒 𝐂
𝐈= 𝛆˳𝐄𝐑𝐌𝐒 𝐂 =
𝛍˳
MOMENTUM OF ELECTROMAGNETIC WAVE
E = mC 2 E = h𝛄
E γ = Frequency
m= 2
C E= Energy of photon
EC h= Planck's constant
p = mC = 2
C p= momentum
𝐄 𝐡 C = Speed of light
𝐩= =
𝐂 𝛌
HERTZ’S EXPERIMENT
In 1865 Maxwell had predicted the propagation of electromagnetic waves in the
form of varying electric and magnetic fields, which produce each other It was
concluded that the accelerated charge is the source of electromagnetic waves.
ELECTROMAGNETIC SPECTRUM
Radio oscillating
> 0.1 m (i)Radio waves are used for wireless
electric communication purposes They are used to
circuits transmit radio signals
having an (ii) Radio waves are used in radio astronomy
inductor and
a capacitor
Microwave 0.1m to oscillating (i)Microwaves are used in the study of
1mm electric atomic and molecular structure
circuits or (ii)Microwaves are used in radar systems.
magnetron (iii)Microwaves are used in long distance
valve telephone communication systems.
(iv)Microwave ovens are used for cooking.
Infra-red 1mm to Vibration of (i)Infra-red rays are used for taking
700 nm atoms and photographs during the conditions of fog,
molecules smoke, etc
(ii)Infra-red rays absorption spectra is
used in the study of molecular structure
and then to check the purity of the
chemicals.
(iii)Used in remote switches in electronic
system such as TV.