E = E_o sin(kx – ωt)
ω = ck
ω = 3 x 10⁸ x 10⁶
ω = 3 x 10¹⁴  rad s^-1 

\(B_o=\frac{E_o}{C}=\frac{\sqrt2E_{rms}}{C}\)
\(B_o=\frac{\sqrt2 \times 3}{3 \times10^8}=1.414 \times10^{-8}T\)

(i) Speed of Electromagnetic wave \(=\frac{Peak\ value\ of\ Electric\ field}{Peak\ value\ of\ magnetic\ field}\)
\(c=\frac { { E }_{ 0 } }{ { B }_{ 0 } } \)
(ii) Yes, As Electromagnetic waves contain both electric and magnetic fields, there is a non-zero energy density associated with it.
\(E=\frac { hc }{ \lambda } \)
Momentum p \(=\frac{Total\ energy\ transferred\ to\ the\ surface}{Velocity\ of\ light\ in\ vacuum}\)
i.e.p = \(\frac{U}{c}=mc\)
U - total energy transferred to the surface.
EM waves carry not only energy and momentum but also angular momentum.

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.

Inductance  L = 1μH = 1\(\times\)10^-6 H
Capacitance C = 1μF = 1 \(\times\)10^-6 F
∴ Frequency \(f =\frac{1}{2 \pi \sqrt{L C}} \)
\(f =\frac{1}{2 \pi \sqrt{1 \times 10^{-6} \times 1 \times 10^{-6}}} \)
Frequency of electromagnetic wave, f \(=\frac{1}{2 \pi \times 10^{-6}} Hz\)
∴ Wavelength of electromagnetic wave (⋋) = \(\frac{C}{f}\)
\(⋋ = 3 \times 10^8 \times 2\pi \times10^{-6}\)
\(=6.28 \times 10^{-6} \times 3 \times 10^{8} \)
Wavelength, ⋋ = 18.84 x 10² m

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.

\(\oint _l\vec{B} \cdot \overrightarrow{d l}=\mu_{o} i_{\text {c }}+\mu_{o} \varepsilon_{o} \frac{d}{d t} \oint _s \vec{E} \cdot \overrightarrow{d A}\)

The displacement current can be defined as the current which comes into play in the region in which the electric field or the electric flux is changing with time.

(a) 10⁹ Hz - Radiowaves
Application: For radio & television communication.
(b) 10¹¹ Hz - microwaves
Application: used in Radar for aircraft navigation, (microwave oven for cooking).

Conduction current Ie = Displacement current ID
\({ I }_{ C }={ I }_{ s }=\frac { dq }{ dt } =\frac { d }{ dt } ({ q }_{ 0 }cos2\pi \gamma t)\)
\(=-2\pi { q }_{ 0 }\gamma sin2\pi \gamma t\)

(i) It is produced by transitions of atomic nuclei and decay of certain elementary particles. They produce chemical reactions on photographic plates, fluorescence, ionization, diffraction.
(ii) Gamma rays provide information about the structure of atomic nuclei. It is used in radiotherapy for the treatment of cancer and tumor, in the food industry to kill pathogenic microorganisms.

Power of the pulse P = 60 x 10^-3 W
Time internal t = 10^-6 S
Energy U = Power x time
U = p x t
= 60 x 10^-3 x 10^-6
U = 60 x 10^-9 J
Lineral momentum, \(\mathrm{P}=\frac{\text { Energy }}{\text { speed }}=\frac{U}{C} \ \)
\(\mathrm{P}=\frac{60 \times 10^{-9}}{3 \times 10^{8}} \)
P = 20 x 10^-17 kg ms^-1

Given: Displacement current,
\({ I }_{ d }={ \varepsilon }_{ 0 }\frac { d{ \phi }_{ E } }{ dt } \)
\(={ \varepsilon }_{ 0 }\frac { d(EA) }{ dt } \quad (\therefore { \phi }_{ E }=EA)\)
\({ I }_{ d }={ \varepsilon }_{ 0 }A\frac { d }{ dt } \left( \frac { V }{ d } \right) \left( \because E=\left( \frac { V }{ d } \right) \right) \)
\({ I }_{ d }=\frac { { \varepsilon }_{ 0 }A }{ d } \left( \frac { dV }{ dt } \right) (\because C=\frac { { \varepsilon }_{ 0 }A }{ d } )\)
Formula:
\({ I }_{ d }=C.\frac { dV }{ dt } \)
Solution: 
\(\frac { dV }{ dt } =\frac { { I }_{ d } }{ C } =\frac { 1.0 }{ 1\times { 10 }^{ -6 } } ={ 10 }^{ 6 }\) 

Since displacement current = conduction current
\({ I }_{ d }=\frac { V }{ { X }_{ C } } =\frac { 220 }{ 100 } =2.2A\)

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.

(i) We have stated Ampere's law as \(\oint \vec{B} \cdot \overrightarrow{d l}=\mu_oi\)
(ii) Where, i is the electric current crossing a surface bounded by a closed curve and the line integral of \(\vec{B}\) is calculated along that closed curve. This equation is valid only when the electric field at the surface does not change with time.
(iii) Maxwell strongly believed that when the time varying magnetic field produces an electric field, the time varying electric field must produce a magnetic field.
(iv) To understand how a varying electric field produces magnetic field, let us consider a situation of charging a parallel plate capacitor.

(v) Let i_c be the conduction current. To calculate the magnetic field at P (fig. 1 ) an amperian loop. S₁ is drawn. Applying Ampere circuital law for the surface S₁, we get
\(\oint \vec{B} \cdot \overrightarrow{d l}=\mu_0 i_c\) Where, \(\mu_0\) is permeability of free space.
(vi) Applying the same for the surface S₂, we get \(\oint \vec{B} \cdot \overrightarrow{d l}=0.\)
Because the surface S₂ nowhere touches the wire carrying conduction current. Therefore for the point P at one surface (S₁) it has some value and at another surface (S₂) it has zero value.
(vii) So, Maxwell believed that there must be a current associated with the changing electric field in between the capacitor and he called that current as displacement current.
(viii) Applying Gauss law to the electric flux between the plates of the capacitor \(\phi_E=\oint \vec{E} \cdot \overrightarrow{\mathrm{dA}}=E A=\frac{q}{\varepsilon_0}\) where, A is the area of the plate.
The change in electric flux is \(\frac{d \phi_F}{d t}=\frac{1}{\varepsilon_0} \frac{d q}{d t} (or) \frac{\mathrm{dq}}{\mathrm{dt}}=\mathrm{i}_{\mathrm{d}}=\varepsilon_0 \frac{\mathrm{d} \phi_{\mathrm{E}}}{\mathrm{dt}}\), where i_d is the displacement current.
(ix) The displacement current can be defined as the current which comes into play in the region in which the electric field and electric flux are changing with time.
(x) So, Maxwell modified Ampere's law \(\oint_{l} \vec{B} \cdot d \vec{l}=\mu_{0} i_c+\mu_{0}-i_d\) which means the total current enclosed by the surface is sum of conduction current and displacement current.