It is produced by Sun, arc, and ionized gases. The wavelength range is 6 x 10^-10m to 4 x 10^-7m and the frequency range is 5 x 10¹⁷Hz to 7 x 10¹⁴Hz. It has less penetrating power. It can be absorbed by atmospheric ozone and harmful to human body. It is used to destroy bacteria, sterilizing the surgical instruments, burglar alarm, detect the invisible writing, finger prints and also in the study of molecular structure.

Amplitude of magnetic field B = 10^-5 T
Frequency, f = 10¹⁰ HZ
(i) Wavelength of the wave,
\({\lambda}=\frac{c}{f} =\frac{3 \times 10^8}{ 10^{10}} \)
= 3 x 10^{8 - 10}
Wavelength = 3 x 10^-2 m
(ii) Electric field E(x,t)\(\hat i\)
Angular frequency \(\omega =2 \pi f \)
\(\omega=2 \times 3.14 \times 10^{10}=6.28 \times 10^{10} rads^{-1}\)
\(k=\frac{2 \pi}{\lambda} =\frac{2 \times 3.14}{3 \times 10^{-2}} \)
\(=\frac{6.28}{3 \times 10^{-2}}=\frac{628}{3}=2.09 \times 10^{2} \)
k = 2.09 x 10²
(iii) E_o = B_oC
E_o = 10^-5 x 3 x 10⁸
E_o = 3 x 10³ V m^-1
The required expression for electric field is
\(\vec{E}(x, t)=E_o \sin \left(\frac{2 \pi}{\lambda} x-2 \pi f t\right) \hat{i} N C^{-1} \)
\(\vec{E}(x , t)=3 \times 10^{3} \sin \left(2.09 \times 10^{2} \mathrm{x}-6.28 \times 10^{10} \mathrm{t}\right) \hat(-{k}) N C^{-1} \)

Potential difference between the plates of the capacitor,
\(V=V_{\max } \sin 2 \pi f t\) 
\(=230 \sqrt{2} \sin (2 \pi \times 50 t)\) 
\(\therefore V=325 \sin 100 \pi t\) 
d = 1 mm = 1 x 10^–3 m
A = 20 cm² = 20 x 10^–4 m²
Displacement current, \(i_{d}=\epsilon_{0} \frac{d \Phi_{E}}{d t}=\epsilon_{\circ} \frac{d(\mathrm{EA})}{d t}\) 
\(\therefore i_{d}=\frac{\epsilon_{0} A}{d}\left[\frac{d V}{d t}\right] \quad\left[\because E=\frac{V}{d}\right]\) 
\(=\frac{\epsilon_{0} A}{d}(325)(100 \pi) \cos 100 \pi t\)
\(=\left(\begin{array}{l} 8.85 \times 10^{-12} \times 20 \times 10^{-4} \times 325 \\ \times 100 \times 3.14 \times \cos (100 \pi \times 1) \end{array}\right) /\left(1 \times 10^{-3}\right)\) 
\(\begin{aligned}=1.81 \times 10^{-6} \mathrm{~A}=1.81 \mu \mathrm{A}[\because \cos (100 \pi \times 1)=1] \end{aligned}\)

Displacement of does not arise due to motion of charge carries but it arises due to time variation of electric flux.

Infrared radiation waves are produced by hot bodies and molecules so it is referred as heat waves. (eg. Sun)
(i) Electromagnetic waves having shorter λ than Infrared radiation are visible, U - v, X-rays, and ૪ - rays.
(ii) Electromagnetic waves having longer λ than Infrared radiation are microwaves, radiowaves.

It is used in radar systems for aircraft navigation, speed of the vehicle, microwave oven for cooking, and very long-distance wireless communication through satellites.

It is used in radio and television communication systems and also in cellular phones to transmit voice communication in the ultra high frequency band.

When the spectrum obtained from the Sun is examined, it consists of large number of dark lines (line absorption spectrum). These dark lines in the solar spectrum are known as Fraunhofer lines.

Given : Frequency of ૪ - rays = 3 x 10²⁰ Hz
Formula:
Energy of gamma rays,
E = h૪
= 6.63 x 10^-34 x 3 x 10²⁰
E = 19.8 x 10^-14 J
∵ [ 1 eV = 1.6 x 10 - 19J; 1 T = \(\frac{1}{1.6\times 10^{-19}}\)  eV]
Solution:
\(E=\frac { 19.8\times { 10 }^{ -14 } }{ 1.6\times { 10 }^{ -19 } } \)
E = 1.24 x 10⁶ eV

(i) Wavelength \(\lambda =\frac { c }{ \gamma } =\frac { 3\times { 10 }^{ 8 } }{ 1.5\times { 10 }^{ 10 } } =2\times { 10 }^{ -2 }m\)
(ii) \(B=\frac { E }{ c } =\frac { 36 }{ 3\times { 1 }0^{ 8 } } =12\times { 10 }^{ -8 }T\)
Formula: (or) 1.2 x 10^-7T
Average energy of magnetic field \(\overrightarrow { E } \) \({ U }_{ E }=\frac { 1 }{ 2 } .{ \varepsilon }_{ 0 }{ E }^{ 2 }\)
The average energy density of electric field \(\overrightarrow { B } \) \({ U }_{ E }=\frac { 1 }{ 2{ \mu }_{ 0 } } .{ B }^{ 2 }\)
But E = CB & C² = \(\frac { 1 }{ { \mu }_{ 0 }{ \varepsilon }_{ 0 } } \)
\({ U }_{ E }=\frac { 1 }{ 2 } .{ \varepsilon }_{ 0 }{ E }^{ 2 }=\frac { 1 }{ 2 } .{ \varepsilon }_{ 0 }{ (CB) }^{ 2 }\)
\({ U }_{ E }=\frac { 1 }{ 2 } .{ \varepsilon }_{ 0 }.\frac { 1 }{ { \mu }_{ 0 }{ \varepsilon }_{ 0 } } { B }^{ 2 }=\frac { 1 }{ { \mu }_{ 0 }{ \varepsilon }_{ 0 } } { B }^{ 2 }={ U }_{ B }\)
\(\therefore { U }_{ E }={ U }_{ B }\)

Absorption spectra:
When light is allowed to pass through a medium or an absorbing substance then the spectrum obtained is known as absorption spectrum. It is the characteristic of absorbing substances. Absorption spectrum is classified into three types:
(i) Continuous absorption spectrum:
When we pass white light through a blue glass plate, it absorbs all the colours except blue and gives continuous absorption spectrum.
(ii) Line absorption spectrum:
When light from the incandescent lamp is passed through cold gas (medium), the spectrum obtained through the dispersion due to prism is line absorption spectrum . Similarly, if the light from the carbon are is made to pass through sodium vapour, a continuous spectrum of carbon are with two dark lines in the yellow region are obtained.
(iii) Band absorption spectrum:
When the white light is passed through the iodine vapour, dark bands on continuous bright background is obtained. This type of band is also obtained when white light is passed through diluted solution of blood or chlorophyll or through certain solutions of organic and inorganic compounds.

Emission spectra:
When the spectrum of self luminous source is taken, we get emission spectrum. Each source has its own characteristic emission spectrum. The emission spectrum can be divided into three types:
(i) Continuous emission spectra (or continuous spectra) :
(a) If the light from incandescent lamp (filament bulb) is allowed to pass through prism (simplest spectroscope), it splits into seven colours.
(b) Thus, it consists of wavelengths containing all the visible colours ranging from violet to red (in the figure). Examples: spectrum obtained from carbon arc, incandescent solids.
(ii) Line emission spectrum (or line spectrum) :
(a) Suppose light from hot gas is allowed to pass through a prism, line spectrum is observed. Line spectra are also known as discontinuous spectra. The line spectra consists of  sharp lines of definite wavelengths or frequencies.
(b) Such spectra arise due to excited atoms of elements. These lines are the characteristics of the element  and are different for different elements. Examples: spectra of atomic hydrogen, helium, etc.
(iii) Band emission spectrum (or band spectrum) :
(a) Band spectrum consists of several number of very closely spaced spectral lines which overlapped together forming specific bands which are separated by dark spaces.
(b) This spectrum has a sharp edge at one end and fades out at the other end. Such spectra arise when the molecules are excited.
(c) Band spectrum is the characteristic of the molecule hence, the structure of the molecules can be studied using their band spectra. Examples, spectra of hydrogen gas, ammonia gas in the discharge tube, etc.

(i) Any stationary source charge produces only electric field. When the charge moves with uniform velocity, it produces steady current which gives rise to magnetic field (not time dependent, only space· dependent) around the conductor in which charge flows.
(ii) If the charged particle accelerates, it produces magnetic field in addition to electric field. Both electric and magnetic fields are time varying fields. Since the electromagnetic waves are transverse waves, the direction of propagation of electromagnetic waves is perpendicular to the plane containing electric and magnetic field vectors.

(iii) Any oscillatory motion is also an accelerating motion, so, when the charge oscillates (oscillating molecular dipole) about their mean position as shown in Figure, it produces electromagnetic waves.
(iv) Suppose the electromagnetic field in free space propagates along z-direction, and if the electric field vector points along x-axis then the magnetic field vector will be mutually perpendicular to both electric field and the direction of wave propogation. Thus,
E_x = E_o sin (k_z - ωt)
B_y = B_o sin(K_z - ωt)
Where, E_o and B_o are amplitude of the oscillating electric and magnetic field, k is a wave number, ω is the angular frequency of the wave and \(\hat { k } \) (unit vector, here it is called propagation vector) denotes the direction of propagation of electromagnetic wave.
(vi) Note that both electric field and magnetic field oscillate with a frequency (frequency of electromagnetic wave) which is equal to the frequency of the source (here, oscillating charge is the source for the production of electromagnetic waves). In free space or in vacuum, the ratio between E_o and B_o is equal to the speed of electromagnetic wave, which is equal to speed of light c.
\(c=\frac { { E }_{ 0 } }{ { B }_{ 0 } } \) 
In any medium, the ratio of E_o and B_o is equal to the speed of electromagnetic wave in that medium. Thus,
\(\mathrm{v}=\frac{E_o}{B_0}< c\)
Further, the energy of electromagnetic waves comes from the energy of the oscillating charge.

(i) Electromagnetic waves are produced by any accelerated charge
(ii) Electromagnetic waves do not require any medium for propagation. So electromagnetic wave is a non mechanical wave.
(iii) Electromagnetic waves are transverse in nature. This oscillating electric field vector, oscillating magnetic field vector and propagation vector (gives direction of propagation) are mutually perpendicular to each other. 
(iv) Electromagnetic waves travel with speed which is equal to the speed of light in vacuum or free space,
\(c =\frac{1}{\sqrt{\varepsilon_{o} \mu_{o}}} \)
\(=3 \times 10^{8} \mathrm{~ms}^{-1} \)
where ε_o is the permittivity of free space or vacuum and μ_o is the permeability of free space or vacuum.
(v) In a medium with permittivity ε and permeability μ, the speed of electromagnetic wave is less than speed in free space or vacuum, that is, v < c.
In a medium of refractive index, \(\mu=\frac{c}{v} \)
n \(=\frac{\frac{1}{\sqrt{\varepsilon_{o} \mu_{o}}}}{\frac{1}{\sqrt{\varepsilon \mu}}} =\sqrt{\varepsilon_{r} \mu_{r}} \)
where ε_r is the relative permittivity of the medium (also known as dielectric constant) and μ_r is the relative permeability of the medium
(vi) Electromagnetic waves are not deflected by electric field or magnetic field.
(vii) Electromagnetic waves can exhibit interference, diffraction and polarization.
(viii) Like other waves, electromagnetic waves also carry energy, linear momentum and angular momentum.
(ix) If the electromagnetic wave incident on a material surface is completely absorbed, then the energy delivered is U and momentum imparted on the surface is \(p=\frac{U}{C}\)
(x) If the incident electromagnetic wave of energy U is totally reflected from the surface, then the momentum delivered to the surface is
\(\Delta p=\frac{U}{C}-\left(-\frac{U}{C}\right)=2 \frac{U}{C}\)