\( { E } ={ E }_{ 0 }\hat { k } \) and \({ B } ={ B }_{ 0 }\hat { j } \)

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

UV light is absorbed by the ozone layer
(i) Source: Sun, arc and ionized gases.
(ii) Uses: To destroy bacteria, sterilizing the surgical instruments, burglar alarm etc

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.

Area of the capacitor = A
Radius = R
Current in the wire connected to the plates I = 5 A
The electric field, between the plates of a parallel plate capacitor,
\(E=\frac{\sigma}{\varepsilon_0}  \)
\(E=\frac{Q}{A \varepsilon_0}\)
Q is the charge accumulated at the positive plate.
The flux of this field, \(\phi_E=\frac{Q}{A \varepsilon_0} \times A=\frac{Q}{\varepsilon_0}\)
Displacement current \(i_d=\varepsilon_0 \frac{d \phi_E}{d t}\)
\(=\varepsilon_0 \frac{d}{d t}\left(\frac{Q}{\varepsilon_0}\right)=i_c\)
\(\therefore \mathrm{i}_{\mathrm{d}}=5 \mathrm{~A} \quad\left(\because\right.\) The current through the capacitor i_c = 5 A)
Displacement current = 5 A

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.

An electromagnetic waves are the waves that are radiated by an accelerated charge which propagates through space as coupled electric and magnetic fields, oscillating perpendicular to each other and to the direction of propagation of the wave.

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

(a) X - rays are used as diagnostic tool in medicine. X-rays are used extensively in studying structures of inner atomic electron shells and crystal structures. It is used in detecting fractures, diseased organs, formation of bones and stones, observing the progress of healing bones. Further, in a finished metal product, it is used to detect faults, cracks, flaws and holes.
(b) Radio are produced by oscillators in electric circuits. It obeys reflection and diffraction. It is used in radio and communication system and cellphones.

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
\(\vec{E}(x, t)=E_o \sin \left(\frac{2 \pi}{\lambda} x-2 \pi f t\right) \hat{i} N C^{-1} \)
\(\vec{E}(x , t)=3 \times 10^{3} \sin \left(2.09 \times 10^{2} \mathrm{x}-6.28 \times 10^{10} \mathrm{t}\right) \hat(-{k}) N C^{-1} \)

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

Given: The amplitude of magnetic field of an Electromagnetic wave B = 1.6 x 10^-7 T
To find:
The amplitude of electric field of an Electromagnetic wave E = ?
frequency ૪ = 30 Mhz = 30 x 10⁶ Hz.
To find: Angle velocity ω =?
Wavelength of Electromagnetic wave λ = ?
(i) Ampere of electric field E = ?
\(\frac { E }{ B } =C\Rightarrow E=C.B\Rightarrow 3\times { 10 }^{ 8 }\times 1.6\times { 10 }^{ -7 }\)
E = 48Vm^-1.
(ii) Angle velocity, ω = 2π૪
ω = 2 x 3.14 x 30 x 10⁶
ω = 1.885 x 10⁸ rad /s.
(iii) Wavelength of Electromagnetic wave, λ = \(\frac{C}{\gamma}\)
\(\gamma=\frac{3\times 10^8}{30\times 10^6}\) = 10m
λ = 10m

(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
\(\Delta p=\frac{U}{C}-\left(-\frac{U}{C}\right)=2 \frac{U}{C}\)

(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.