Here students can locate TS Inter 2nd Year Physics Notes 11th Lesson Electromagnetic Waves to prepare for their exam.

## TS Inter 2nd Year Physics Notes 11th Lesson Electromagnetic Waves

→ Electromagnetic waves: Electromagnetic waves consists of time varying electric and magnetic field. A time varying electric field will produce a magnetic field and vice versa. In this way in electromagnetic waves energy oscillates between electric and magnetic fields.

→ Ampere-Maxwell Law: The total current passing through any surface of which the closed loop as the perimeter is the sum of conduction current and the displacement current.

i.e ∮\(\overline{\mathrm{B}} \cdot \mathrm{d} \bar{l}\) = μ_{0} + μ_{0}ε_{0} \(\frac{\mathrm{d} \phi_E}{\mathrm{dt}}\)

→ Displacement current: According to Maxwell a time changing electric flux through a surface will also generate a current. This current produced due to rate of change in electric flux is called displacement current i_{d}.

Its value Is ε_{0} times greater than \(\frac{\mathrm{d} \phi_E}{\mathrm{dt}}\)

Displacement current, i_{d} = ε_{0}\(\frac{\mathrm{d} \phi_E}{\mathrm{dt}}\)

where \(\frac{\mathrm{d} \phi_{\mathrm{E}}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left(\frac{\mathrm{Q}}{\epsilon_0}\right)=\frac{1 \mathrm{dQ}}{\epsilon_0} \frac{\mathrm{dt}}{\mathrm{dt}}\)

But \(\frac{\mathrm{d} \phi}{\mathrm{dt}}\) = Rate of change of charge displacement current i_{d}

→ Conduction current (i_{c}): Current carried by conductors due to flow of charges is called “conduction current” (i_{c}).

Note:

- From Maxwell’s theory total current ‘i’ is the sum of conductiqn current i
_{c}and displacement current i_{d}.

i = i_{c}+ i_{d} - There are many regions in space which contains only displacement current due to time varying electric fields.
- From Maxwell’s theory the source of magnetic field is not just due to conduction current produced by flow of charges. Magnetic field can also be produced due to time rate of change of electric field.

→ Electromagnetic waves (Maxwell’s concepts):

- According to Maxwell’s theory, accelerated charges radiate electromagnetic waves.
- These electric and magnetic fields are mutually perpendicular and also perpendicular to direction of propagation.
- Frequency of electromagnetic wave is equal to frequency of oscillator.
- Energy associated with the propagation of wave is obtained from oscillating source.
- In an electromagnetic wave let electric field vibrations are along X-axis and magnetic field vibrations are along Y -axis then direction of propagation of electromagnetic wave is along Z-axis.
- Electric field component E
_{x}= E_{0}sin (kz – cot)

Magnetic field component B_{y}= B_{0}sin (kz – cot)

where k = \(\frac{2 \pi}{\lambda}\) and speed of wave v = \(\frac{\omega}{k}\).

→ From Maxwell’s equations relation between

E_{0} and B_{0} is \(\frac{\mathrm{E}_0}{\mathrm{~B}_0}\) = c or B_{0} = \(\frac{E_0}{c}\)

→ In vacuum velocity of electromagnetic wave c = \(\frac{1}{\sqrt{\mu_0 \epsilon_0}}\)

→ In a medium velocity of electromagnetic v =\(\frac{1}{\sqrt{\mu \epsilon}}\)

→ Hertz experiments on electromagnetic waves showed that electromagnetic waves of wavelength 10 million times more than light waves could be diffracted, reflected and polarised.

→ Electromagnetic waves carry energy and momentum like other waves.

→ Amount of pressure of visible light is in the order of 7 × 10^{-6} N / m^{2}.

→ Electromagnetic spectrum: Electromagnetic spectrum extends over a wide wavelength region of 107 m to 10-14 m. It consists of longer wavelength radio waves. Television and F.M Radio waves, Microwaves, Infrared, Visible and Ultra violet light, X-Rays and high energetic y – Rays.

→ Radio waves: Radio waves are produced by the accelerated motion of charges in conducting wires. They are generally in the range of 500 kHz to 1000 MHz.

- Amplitude Modulation is in the range of 530 kHz to 1710 kHz.
- Short waves are lip to 54 MHz.
- TV signals range is 54 MHz to 890 MHz.

→ Microwaves: Frequency of microwaves is in the region of gegahertz. They are produced by klystrons and magnetrons.

In Microwave ovens the frequency of magnetron is matched to resonant frequency of water molecules. So that energy of microwaves is rapidly and efficiently transferred to food material containing water molecules and their temperature rises quickly.

→ Infrared waves: Infrared rays are produced by hot bodies and molecules. Their wave-length is in the range of 1 mm to 700 nm.

Infrared rays plays an important role in keeping warm atmosphere of earth through green house effect.

→ Visible light The part of electromagnetic spectrum that can be detected by human eye is called visible spectrum. Wavelength range of visible spectrum is 700 nm to 400 nm. Note: Snakes can defect. infrared rays. Many insects can detect ultraviolet rays.

→ Ultraviolet rays: Wavelength range of ultra-violet rays is 400 nm to 0.6 nm. They are more energetic. Exposure to UV rays will cause tanning to skin. They cannot travel through glass. In atmosphere Ozone layer in upper atmosphere filters UV rays.

→ X-rays: Wavelength range of X-rays 10^{-10} nm to 10^{-4} nm. Commonly used method to produce X-rays is to bombard metal target with high energy electrons. X-rays are widely used as diagnostic tools in medicine.

→ Gamma rays: Wavelength range of gamma rays is 10-10 nm to 10~14 nm. They are very high energetic radiation. These rays are produced in nuclear reactions and also by radio active nuclie.

In medicine they are used to destroy cancer cells.

→ Electric flux Φ_{E} = \(\frac{\mathrm{Q}}{\epsilon_0}\)

→ Displacement current i = e_{0}\(\left(\frac{\mathrm{d} \phi_{\mathrm{E}}}{\mathrm{dt}}\right)\)

→ Ampere – Maxwell’s Law

∮\(\overline{\mathrm{B}} \cdot \mathrm{d} \bar{l}\) = μ_{0} + μ_{0}ε_{0} \(\frac{\mathrm{d} \phi_E}{\mathrm{dt}}\)

→ Maxwell’s equations

(a) \(\oint \overline{\mathrm{E}} \cdot \mathrm{d} \overline{\mathrm{A}}=\frac{\mathrm{Q}}{\epsilon_0}\) (Gauss law for Electricity)

(b) \(\oint \overline{\mathrm{B}} \cdot \mathrm{d} \overline{\mathrm{A}}\) = 0 (Gauss Law for Magnetism)

(c) \(\oint \overline{\mathrm{E}} \cdot \mathrm{d} \bar{l}=\frac{-\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\) (Faraday’s Law)

(d) ∮\(\overline{\mathrm{B}} \cdot \mathrm{d} \bar{l}\) = μ_{0} + μ_{0}ε_{0} \(\frac{\mathrm{d} \phi_E}{\mathrm{dt}}\)

(Ampere-Maxwell’s Law)

→ In Electromagnetic waves

(a) Electric field E_{x} = E_{0} sin (kz – ωt)

(b) Magnetic field B_{y} = B_{0} sin (kz – ωt)

(c) Speed of wave v = \(\frac{\omega}{k}\), ω = ck where k = \(\frac{2 \pi}{\lambda}\)

(d) Velocity of electromagnetic wave in vacuum c = \(\frac{1}{\sqrt{\mu_0 \in_0}}\).

(e) Velocity of electromagnetic wave in medium c = \(\frac{1}{\sqrt{\mu \epsilon}}\).

→ In electromagnetic waves \(\frac{\mathrm{E}_0}{\mathrm{~B}_0}\) = C or B_{0} = E_{0}c

where E_{0} and B_{0} are magnitudes of electric field and magnetic field in vacuum.