EM waves

 1. Need for Displacement Current

Ampere’s circuital law for conduction current during charging of a capacitor was found inconsistent. Therefore, Maxwell modified Ampere’s circuital law by introducing displacement current. It is given by Id=ε0dφEdt

Modified Ampere’s circuital law is:

∮B⃗ .dl⃗ =μ0(I+ε0dφEdt)

where φE = electric flux.

2. Electromagnetic Waves

The waves propagating in space through electric and magnetic fields varying in space and time simultaneously are called electromagnetic waves.

The electromagnetic waves are produced by an accelerated or decelerated charge or LC circuit. The frequency of em waves is

ν=12πLC√

3. Characteristics of Electromagnetic Waves

(i) The electromagnetic waves travel in free-space with the speed of light (c = 3 × 108 m/s) irrespective of their wavelength.

(ii) Electromagnetic waves are neutral, so they are not deflected by electric and magnetic fields.

(iii) The electromagnetic waves show properties of reflection, refraction, interference, diffraction and polarisation.

(iv) In electromagnetic wave the electric and magnetic fields are always in the same phase.

(v) The ratio of magnitudes of electric and magnetic field vectors in free space is constant equal to c.

EB=1μ0ε0√=c=3×108m/s

(vi) The speed of electromagnetic waves in a material medium is given by

v=1με√=cμrεr√=cn, where n is the refractive index.

(vii) In an electromagnetic wave the energy is propagated by means of electric and magnetic field vectors in the direction of propagation of wave.

(viii) In electromagnetic wave the average values of electric energy density and magnetic energy density are equal

(12ε0E2)aν=(B22μ0)aν

(ix) The electric vector of electromagnetic wave is responsible for optical effects and is also called the light vector.

(x) Electromagnetic waves carry energy and momentun E=hcλ,p=uc=mc

4. Transverse Nature of Electromagnetic Waves

The electromagnetic waves are transverse in nature. In electromagnetic waves the electric and magnetic fields are mutually perpendicular and also perpendicular to the direction of wave’ propagation, such that E⃗ , B⃗  and K⃗  form a right handed set ( K⃗ is propagation vector along the direction of propagation).

5. Electromagnetic Spectrum

The electromagnetic waves have a continuous wavelength starting from short gamma rays to long radiowaves. The orderly distribution of wavelength of em waves is called the electromagnetic spectrum. The complete spectrum is given in the following table:

S. No.	Name	Wavelength Range (m)	Frequency Range (Hz)
i.	Gamma rays	10–13 – 10–10	3 × 1021 – 3 × 1018
ii.	X-rays	10–10 – 10–8	3 × 1018 – 3 × 1016
iii.	Ultraviolet rays	10–8 – 4×10–7	3 × 1016 – 7.5 × 1014
iv.	Visible light	4 × 10–7 – 7.5 × 10–7	7.5 × 1014 – 4 × 1014
v.	Infra red light	7.5 × 10–7 – 10–3	4 × 1014 – 3 × 1011
vi.	Microwaves	10–3 – 10–1	3 × 1011 – 1010
vii.	Radio waves	10–1 – 104	1010 – 3 × 104

 

6. Wavelength Range of Visible Spectrum

Visible light has a continuous wavelength starting from 400 nm to 750 nm; for convenience it is divided into 7 colours.

V	Violet	400 nm — 420 nm
I	Indigo	420 nm — 450 nm
B	Blue	450 nm — 500 nm
G	Green	500 nm — 570 nm
Y	Yellow	570 nm — 600 nm
O	Orange	600 nm — 650 nm
R	Red	650 nm — 750 nm

 

7. Uses of Electromagnetic Spectrum

(i) γ-rays are highly penetrating, they can penetrate thick iron blocks. Due to high energy, they are used to initiate some nuclear reactions. γ-rays are produced in nuclear reactions. In medicine, they are used to destroy cancer cells.

(ii) X-rays are used in medical diagnostics to detect fractures in bones, tuberculosis of lungs, presence of stone in gallbladder and kidney. They are used in engineering to check flaws in bridges. In physics X-rays are used to study crystal structure.

(iii) Ultraviolet rays provide vitamin D. These are harmful for skin and eyes. They are used to sterilise drinking water and surgical instruments. They are used to detect invisible writing, forged documents, finger prints in forensic lab and to preserve food items.

(iv) Infrared rays are produced by hot bodies and molecules. These waves are used for long distance photography and for therapeutic purposes.

(v) Radiowaves are used for broadcasting programmes to distant places. According to frequency range, they are divided into following groups

(1) Medium frequency band or medium waves 0·3 to 3 MHz

(2) Short waves or short frequency band 3 MHz — 30 MHz

(3) Very high frequency (VHF) band 30 MHz to 300 MHz

(4) Ultrahigh frequency (UHF) band 300 MHz to 3000 MHz

(vi) Microwaves are produced by special vacuum tubes, namely; klystrons, magnetrons and gunn diodes. Their frequency range is 3 GHz to 300 GHz.

They are used in RADAR systems for aircraft navigation and microwave used in homes.