Electromagnetic Waves Notes – Complete Chapter

Displacement Current

Definition

Displacement current is due to time-varying electric field (not actual charge flow)
It acts as a source of magnetic field in exactly the same way as conduction current
This concept was introduced by Maxwell to complete Ampere's Law

i_d = ε₀ × dΦ_E/dt (displacement current)

Generalised Ampere's Law: ∮B·dl = μ₀(i_c + i_d) = μ₀i_c + μ₀ε₀ × dΦ_E/dt

Conduction current i_c flows in wire; displacement current i_d exists between capacitor plates

Law	Equation	Physical Meaning
Gauss's Law for Electricity	∮E·dA = q/ε₀	Electric flux through closed surface = enclosed charge/ε₀
Gauss's Law for Magnetism	∮B·dA = 0	No magnetic monopoles exist; magnetic field lines always form closed loops
Faraday's Law	∮E·dl = −dΦ_B/dt	Time-varying magnetic field induces electric field
Ampere-Maxwell Law	∮B·dl = μ₀i_c + μ₀ε₀ dΦ_E/dt	Current AND time-varying electric field produce magnetic field

Properties of EM Waves

EM waves are produced by accelerating charges (acceleration is absolute, not relative)
An oscillating charge with frequency ν produces EM waves of same frequency ν
Electric dipole is a basic source of EM waves
EM waves are transverse in nature — E and B oscillate perpendicular to each other and to direction of propagation
Do NOT require any material medium for propagation (travel in vacuum)
Speed in vacuum: c = 3×10⁸ m/s (same for all EM waves)
Hertz produced and detected EM waves (wavelength of few metres) in 1887
Electric dipole as a basic source of EM waves

E = E₀ sin(kz − ωt); B = B₀ sin(kz − ωt) (propagating along z-axis)

E₀/B₀ = c (ratio of amplitudes = speed of light)

k = 2π/λ (wave number); ω = 2πν (angular frequency)

c = 1/√(μ₀ε₀) = 3×10⁸ m/s (speed in vacuum)

v = 1/√(με) (speed in medium with permeability μ and permittivity ε)

Energy density: u = ε₀E²/2 + B²/(2μ₀) = ε₀E² (equal parts electric and magnetic)
Energy is shared equally between E and B fields
Intensity (Poynting vector): I = S = E×B/μ₀ = E₀B₀/(2μ₀) (average)
Radiation pressure: P = u = I/c (for completely absorbed) or 2I/c (for completely reflected)
Momentum: p = U/c (where U = total energy transferred)

Order (Increasing Wavelength / Decreasing Frequency)

Gamma rays → X-rays → Ultraviolet → Visible → Infrared → Microwaves → Radio waves

Wavelength range: 10⁻¹²m to 10⁶m (or 10⁻² Å to 10⁶m)

Type	Frequency Range	Wavelength Range	Production	Detection / Uses
Gamma Rays	10¹⁸ – 10²² Hz	<10⁻³ nm = <10⁻¹² m	Radioactive decay of nucleus	Photographic film, Geiger tubes, ionisation chamber; treat cancer, manufacture polyethylene
X-rays	10¹⁸ – 10²⁰ Hz	1 nm – 10⁻³ nm (10⁻⁸ to 10⁻¹³ m)	X-ray tubes or inner shell electrons	Photographic film, Geiger tubes; medical diagnosis
Ultraviolet	10¹⁶ – 10¹⁷ Hz	400 nm – 1 nm (4×10⁻⁷ to 6×10⁻¹⁰ m)	Inner shell electrons moving between energy levels	Photocells, photographic film; LASIK surgery, UV lamps kill germs in water purifiers, welding
Visible Light	4×10¹⁴ – 7×10¹⁴ Hz	700 nm – 400 nm	Electrons in atoms moving from higher to lower energy levels	Eyes, photographic film, photocells
Infrared (Heat waves)	10¹¹ – 5×10¹⁴ Hz	1 mm – 700 nm (5×10⁻³ to 10⁻⁶ m)	Vibration of atoms and molecules; hot bodies; semiconductor LEDs	Thermopiles, bolometer, infrared photographic film; remote switches, greenhouse effect, night vision
Microwaves	10⁹ – 10¹² Hz	0.1 m – 1 mm	Klystron valve, magnetron valve, Gunn diodes	Point contact diodes; radar systems, aircraft navigation, microwave ovens
Radio Waves	500 kHz – 1000 MHz	>0.1 m (600 m to 0.1 m)	Rapid acceleration and deceleration of electrons in aerials	Receiver aerials; radio and TV communication

Sub-bands of Radio Waves

Layer	Approximate Height	Key Features
Troposphere	0 – 12 km	Weather, most of atmosphere mass; clouds form here
Tropopause	~12 km	Boundary between troposphere and stratosphere
Stratosphere	12 – 50 km	Jets fly here; ozone layer present
Ozone Layer	15 – 30 km	Absorbs harmful UV radiation from Sun
Stratopause	~50 km	Boundary between stratosphere and mesosphere
Mesosphere	50 – 80 km	Meteors burn up here
Mesopause	~80 km	Coldest region of atmosphere
Thermosphere / Ionosphere	80 – ~400 km	Contains ionized gases; reflects radio waves back to Earth; includes Kennelly-Heaviside layer and Appleton layer

Ionosphere — Kennelly-Heaviside and Appleton Layers

Ionosphere reflects radio waves back to Earth → enables long-distance radio communication
Kennelly-Heaviside layer and Appleton layer are sublayers within ionosphere
TV signals (high frequency) are NOT reflected by ionosphere → need satellite for long-distance TV
AM radio (long wavelength) is reflected → can travel very long distances