EM Waves Properties & Propagation | Physics Class 12 - NEET PDF Download

Electromagnetic Waves

Electromagnetic waves are those waves in which electric and magnetic field vectors changes sinusoidally and are perpendicular to each other as well as at right angles to the direction of propagation of wave.

The equation of plane progressive electromagnetic wave can be written as 

E = E_o sin Ω (t – x / c) and B = B_o sin Ω (t – x / c). Where, Ω =2πv

Electromagnetic waves are produced by accelerated charge particles.

Properties of EM Waves

(i) These waves are transverse in nature.

(ii) These waves propagate through space with speed of light, i.e., 3 * 10⁸ m / s.

(iii) The speed of electromagnetic wave,

c = 1 / √μ_o ε_o

where, μ_o is permittivity of free space,

∴ c = E_o / B_o

where E_o and B_o are maximum values of electric and magnetic field vectors.

According to Maxwell, when a charged particle is accelerated, it produces electromagnetic wave. The total radiant flux at any instant is given by,

   p = q²a² / 6 πε_oc²

(iv) The rate of flow of energy in an electromagnetic wave is described by the vector S called the poynting vector, which is defined by the expression,

S = 1 / μ_o E * B

SI unit of S is watt/m².

(v) Its magnitude S is related to the rate at which energy is transported by a wave across a unit area at any instant.

(vi) The energy in electromagnetic waves is divided equally between electric field and magnetic field vectors.

(vii) The average electric energy density.

  U_E = 1 / 2 ε_o   E² = 1 / 4 ε_o E²_o

(viii) The average magnetic energy density,

  U_B = 1 / 2 B² / μ_o = 1 / B²_o / μ_o

(ix) The electric vector is responsible for the optical effects of an electromagnetic wave.

(x) Intensity of electromagnetic wave is defined as energy crossing per unit area per unit time perpendicular to the directions of propagation of electromagnetic wave.

(xi) The intensity I is given by the relation,

  I = < μ > c = 1 / 2 ε_o E²_oc

(xii) The existence of electromagnetic waves was confirmed by Hertz experimentally in 1888.

Propagation of Electromagnetic Waves

In radio wave communication between two places. the electromagnetic waves are radiated out by the transmitter antenna at one place which travel through the space and reach the receiving antenna at the other place.

Electromagnetic Spectrum

The arranged array of electromagnetic radiations in the sequence of their wavelength or frequency is called electromagnetic spectrum

Radio and microwaves are used in radio and TV communication,

Infrared rays are used to

(i) Treat muscular straw.
(ii) For taking photographs’ in fog or smoke.
(iii) In green house to keep plants warm.
(iv) In weather forecasting through infrared photography.

Ultraviolet rays are used

(i) In the study of molecular structure.
(ii) In sterilizing the surgical instruments.
(iii) In the detection of forged documents, Eringer prints.

X-rays are used

(i) In detecting faults, cracks, flaws and holes in metal products.
(ii) In the study of crystal structure.
(iii) For the detection of pearls in oysters.

γ – rays are used for the study of nuclear structure.

Solved Examples on EM Waves

Question 1: Calculate the frequency and wavelength of an electromagnetic wave with an energy of 6.626×10⁻¹⁹ J.

Answer:

• Frequency (f):E/h=6.626×10⁻¹⁹/6.626×10⁻³⁴=10¹⁵ Hz.
• Wavelength (λ): $c/f\; =\; \backslash frac\{3\; \backslash times\; 10^8\}\{10^\{15\}\}\; =\; 3\; \backslash times\; 10^\{-7\}$c/f=3×10⁸/10¹⁵=3×10⁻⁷ meters.

Question 2: What are the applications of X-rays?

Answer: X-rays are used in medical diagnostics to detect bone fractures and other ailments. They are also useful for ionization purposes.

Question 3: Are X-rays and gamma rays suitable for broadcasting radio, TV, or mobile signals?

Answer: No, X-rays and gamma rays are unsuitable for broadcasting because they have short ranges and are harmful. Their high penetrating power can damage living tissue.

Question 4: Identify which of the following is not a property of electromagnetic waves:

1. Momentum
2. Energy
3. Pressure
4. Heat energy

Answer:

• 1. Electromagnetic (EM) waves can transfer momentum to materials they interact with.
• 2. EM waves carry energy and can transmit it through a vacuum.
• 3. EM waves exert pressure, as demonstrated by a radiometer, which spins due to light-induced pressure differences.
• 4. EM waves do not carry heat energy, but they can heat objects upon absorption.

Question 5: A sunlight ray passing through your kitchen window hits a prism, creating a rainbow on the windowsill. If you place a radiometer on a specific color of the rainbow and measure the energy as 4.0×10⁻¹⁹ joules, what color might you have measured? Use Planck’s constant $6.6256\; \backslash times\; 10^\{-34\}$6.6256×10⁻³⁴ J·s to determine this.

Answer:

• Equation to use: E=h⋅f

• Solving for frequency (f): $f\; =\; E\; /\; h$f=E/h

• Given:

  • Energy (E) = 4.0×10⁻¹⁹ joules
  • Planck’s constant (h) = $6.6256\; \backslash times\; 10^\{-34\}$6.6256×10⁻³⁴ J·s

• Calculation: $Hzf\; =\; \backslash frac\{4.0\; \backslash times\; 10^\{-19\}\}\{6.6256\; \backslash times\; 10^\{-34\}\}\; \backslash approx\; 6.03\; \backslash times\; 10^\{14\}\; \backslash text\{\; Hz\}$f=4.0×10⁻¹⁹ / 6.6256×10⁻³⁴≈6.03×1014 Hz

This frequency falls within the visible spectrum, near the green color range. Therefore, the measured color is likely green, though it could also be cyan or blue.