electromagnetic waves class 12 pdf notes
★ On the basis of vibration
sinusoidal variation of electric and magnetic field at right angles to each other as well
as at right angles to the direction of wave propagation.
e.g.- x-ray, gamma ray, microwave, radiowave ,infrared, ultraviolet, visible light.
${{B}_{y}}={{B}_{0}}\operatorname{Sin}(\omega
t+kx)$
★ Properties of electromagnetic waves-
1. Electromagnetic waves are produced by accelerated or oscillating charge.
2. These waves do not carry any charge.
3. These waves do not require any medium for propagation.
4. It travels in Straight line.
5. These waves travel in air or free space with a speed of $3\times {{10}^{8}}$ m/s.
In air or free space (vacuum) light also travels with the same speed. So, light is an electromagnetic wave.
6. These Waves are transverse. Hence, they can be polarized.
In these waves, magnetic field and electric field oscillate in
perpendicular directions of wave propagation.
7. These waves carry energy, which is equally divided between electric field and
magnetic field.
8. These waves are not deflected by electric and magnetic fields.
9. Speed of these waves in air or vacuum (according to Maxwell).
${{c}_{0}}=\frac{1}{\sqrt{{{\mu
}_{0}}{{\in }_{0}}}}$
Where-
${{\mu }_{_{0}}}$ = Permeability of vacuum = $4\pi \times {{10}^{-7}}$ H/m
${{\in }_{0}}$ = Permittivity of vacuum = 8.854 × ${{10}^{-12}}{{C}^{2}}/N{{m}^{2}}$
${{c}_{0}}=3\times
{{10}^{8}}$ m/s
10. Speed of these waves in a medium other than air or Vacuum is less than that of
in air or vacuum.
$c=\frac{1}{\sqrt{\mu \in }}$
Where-
$\mu $= Permeability of medium
ε= Permittivity of medium
$c=\frac{1}{\sqrt{{{\mu
}_{0}}{{\mu }_{r}}{{\in }_{0}}{{\in }_{r}}}}$
$c=\frac{1}{\sqrt{{{\mu
}_{0}}{{\in }_{0}}}}\times \frac{1}{\sqrt{{{\mu }_{r}}{{\in }_{r}}}}$
So,
$c=\frac{{{c}_{0}}}{\sqrt{{{\mu
}_{r}}{{\in }_{r}}}}$
11. Electric energy density ( ${{u}_{E}}$
) Magnetic energy density ( ${{u}_{B}}$
)
are as followings-
${{u}_{E}}=\frac{1}{2}{{\in
}_{0}}{{E}^{2}}$
${{u}_{B}}=\frac{1}{2}\frac{{{B}^{2}}}{{{\mu }_{0}}}$
12. According to Maxwell, the ratio of electric field and magnetic field is equal to
velocity of light:
E / B = c
13. Electric field vectors are responsible for the optical effect of electromagnetic
waves. It is called light vector.
14. The frequency of an electromagnetic wave does not change when it goes from
one medium to another medium, but its wavelength changes.
★ Electromagnetic spectrum-The orderly distribution of electromagnetic waves according to their wavelength or frequency is called electromagnetic spectrum.
★ Uses of electromagnetic spectrum-
1. Radio waves-
Production- Oscillating current
Wavelength- 0.3m to $6\times {{10}^{2}}$m
Frequency- $5\times {{10}^{5}}$Hz to ${{10}^{3}}$ Hz
Uses-
a. In Radio and television Communication.
b. In mobile and wireless Communication.
2. Microwaves-
Production- Klystron or Magnetron valve
Wavelength- ${{10}^{-3}}$m to 0.3m
Frequency- ${{10}^{9}}$ Hz to 300x${{10}^{9}}$Hz
Uses-
a. In Radar System.
b. microwaves are used to observing movement of trains.
c. Microwaves are used for Cooking in microwave oven.
3. Infrared-
Production- Excitation of atoms and molecules
Wavelength- 7.5x${{10}^{-7}}$m to ${{10}^{-3}}$m
Frequency- 3x${{10}^{11}}$ Hz to 4x${{10}^{14}}$Hz
Uses-
a. In remote control
b. for photography in dark, fog, smoke.
c. In weather forecasting through infrared photography.
d. In physiotherapy i.e. to treat muscular strain.
e. for producing dehydrated fruits.
4. Visible light-
Production- Excitation of valence electron
Wavelength- 0.27x${{10}^{-7}}$m to 0.75x ${{10}^{-7}}$m
Frequency- 4x${{10}^{14}}$ Hz to 8x${{10}^{14}}$Hz
Uses-
a, To see objects.
b. To watch spectrum
5. Ultraviolet-
Production- Excitation of atoms
Wavelength- 6x${{10}^{-10}}$m to 0,27x ${{10}^{-7}}$m
Frequency- 8x${{10}^{14}}$ Hz to 5x${{10}^{17}}$Hz
Uses-
a. For checking mineral samples.
b. To destroy bacteria.
c. For sterilizing surgical instruments.
d. In fingerprint and forensic lab.
e. In burglar alarm.
6. X-rays -
Production- Sudden retardation of high enerzy electron
Wavelength- ${{10}^{-13}}$m to 3x ${{10}^{-8}}$m
Frequency- ${{10}^{16}}$ Hz to 3x${{10}^{21}}$Hz
Uses-
a. In detection of bone fracture.
b. To cure skin disease.
c. for study crystal structure of complex substance.
d. For detection of explosive, gold in the body of smugglers.
7. Gamma ray-
Production- Nuclear origin
Wavelength- 6x${{10}^{-15}}$m to ${{10}^{-10}}$m
Frequency- 3x${{10}^{18}}$ Hz to 5x${{10}^{22}}$Hz
Uses-
a. To produce nuclear reaction.
b. To preserve food stuff for long time.
c. In the treatment of cancer and tumours.
Displacement Current
Electric current, which is produced due to change of electric flux with time, is called
displacement current.
# let, area of the plate of a capacitor = A
at any moment, charge on the plate= q
surface charge density = σ = q/A
# Electric field between the plates E=
E = σ /ε0
# Electric flux between the plates=
μe = E ·A = EA cosθ = EA cos0= EA
μe = E ·A = EA cosθ = EA
= σ/ε0× A
= q/Aε0 × A = q/ε0
= μe = q/ε0
q =ε0μe
Differentiating w.r.l time
dq /dt = ε0 × dμe /dt
Id = ε0 × dμe /dt
ε0 × dμe /dt is called displacement current by Maxwell.
Maxwell–Ampere Law
Line integral of magnetic field is
μ0 times of the sum of conduction current (Ic) and displacement current (Id)
∮ B ·dl = μ0 (Ic + Id)= μ0 ( dq/dt + ε0 × dμe/dt )
Where:
Ic = conduction current= dq/dt
Id =displacement current= ε0 × dμe/dt
Maxwell’s Equation
Maxwell gave a set of four equation , which are known as Maxwell's equation.
Maxwell equation describe, how an electric field can generate a magnetic
field and vice-versa. These equation give complete description of all electromagnetic
interactions.
1. ∮ E ·dA =Q×1/ε0
This equation is Gauss’s law in electrostatics.
2. ∮ B ·dA = 0
This equation is Gauss's law in magnetism.
3. ∮ E ·dA =dμB/dt
This equation is faraday's law of electromagnetic induction.
4. ∮ B ·dl = μ0 (Ic + Id)
This equation represents Ampere- Maxwell's law.
# Lorentz force- Force on a charge particle, when it is in electric and magnetic both
field simultaneously, is called Lorentz force.
F= q [ Ē +( V × B)]
four Maxwell's equation and Lorentz force represent all electromagnetic interaction.
Hertz experiment Maxwell theoretically predicted electromagnetic waves in 1865.
Hertz experimentally Confirmed their existance in 1888.
# Principle- An oscillating charge radiates electromagnetic waves and these waves
carry energy, which is being supplied at the cost of Kinetic energy of Oscillating
Charge.
# Hertz apparatus- A and B are two large square metal plates of copper or zinc
placed apart (almost 60cm apart). They are Connected to two highly polished metallic
sphere S1 and S2 through thick copper wires which are about 2-3cm apart.
S1 and S2 are connected to induction coils.
An another unclosed metallic ring hang small metallic spheres S1and S2
with some gap. This ring is called detector. Here S1,S2 are parallel to each-other.
# Working- A high potential difference of several thousand volts is applied across
the spheres S1 and S2 using Induction Cal. Due to high potential difference across S1
and S2 , the air between spheres get ionised. Due to it, a spark is produced between S1
and S2 and electromagnetic waves of high frequency are produced.
Here the two plates act as Capacitor having a small capacitance C and
the connecting wire provide the law inductance L. The high frequency of oscillation
of charge between the plates is given by
ƒ = 1/ 2π √LC
The detector is also held in a position such that a spark between S1 and S2 due to
transfer of electromagnetic waves.
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