1. Displacement Current
Displacement current is a quantity that is defined in terms of the rate of change of electric flux. It plays a crucial role in making Ampere's law consistent for time-varying electric fields.
\[ I_D = \varepsilon_0 \frac{d\phi_e}{dt} \]
Where:
- ID = displacement current
- ε0 = permittivity of free space
- dΦe/dt = rate of change of electric flux
Ampere-Maxwell Circuital Law
The modified form of Ampere's law that includes displacement current:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 \left( I_C + \varepsilon_0 \frac{d\phi_e}{dt} \right) \]
Where IC is the conduction current.
Key Properties of Displacement Current:
- The conduction current and displacement current are always equal in magnitude: IC = ID
- Like conduction current, displacement current is also a source of magnetic field
- Displacement current exists even in vacuum where there are no charges
- It completes the current circuit through capacitors
1.1 Production of Electromagnetic Waves
According to Maxwell's theory, an accelerated charge produces electromagnetic waves by setting up time-varying electric and magnetic fields that act as sources for each other.
- An accelerated charge sets up a varying magnetic field in its neighborhood
- This varying magnetic field produces a varying electric field
- Both fields vary with time and sustain each other
- The coupled electric and magnetic fields propagate through space as electromagnetic waves
2. Properties of Electromagnetic Waves
Wave Equation for Electromagnetic Waves
\[ \frac{\partial^2 E}{\partial x^2} = \mu_0 \varepsilon_0 \frac{\partial^2 E}{\partial t^2} \]
Fundamental Properties:
- Speed in vacuum: Electromagnetic waves travel through vacuum with speed of light:
\[ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = 3 \times 10^8 \, \text{m/s} \]
- Transverse nature: Electric and magnetic fields are perpendicular to each other and to the direction of propagation
- Field relationship: The instantaneous magnitudes of E and B are related by:
\[ \frac{E}{B} = c \]
2.1 Energy and Momentum of EM Waves
The Poynting vector describes the rate of energy flow per unit area in electromagnetic waves.
\[ \vec{S} = \frac{1}{\mu_0} \vec{E} \times \vec{B} \]
Electromagnetic waves carry both energy and momentum, which leads to radiation pressure:
\[ \text{For perfect absorber: } P = \frac{S}{c} \]
\[ \text{For perfect reflector: } P = \frac{2S}{c} \]
2.2 Sinusoidal Plane Electromagnetic Waves
For a sinusoidal plane wave propagating in the positive x-direction:
\[ E = E_m \sin (kx - \omega t) \]
\[ B = B_m \sin (kx - \omega t) \]
Where:
- ω = 2πf (angular frequency)
- k = 2π/λ (wave number)
Intensity of EM Waves
\[ S_{av} = \frac{E_m B_m}{2\mu_0} = \frac{E_m^2}{2\mu_0 c} = \frac{c}{2\mu_0} B_m^2 \]
3. Electromagnetic Spectrum
The electromagnetic spectrum is the orderly distribution of electromagnetic waves according to their wavelength or frequency, forming distinct groups with different properties and applications.
3.1 Complete Electromagnetic Spectrum
| Radiation | Discoverer | Production | Wavelength Range | Frequency Range | Energy Range | Properties | Applications |
|---|---|---|---|---|---|---|---|
| Gamma Rays | Becquerel & Curie | Radioactive decay of nuclei | 10⁻¹⁴ m to 10⁻¹⁰ m | 3×10²² Hz to 3×10¹⁸ Hz | 10⁶ eV | High penetrating power, uncharged, low ionizing power | Nuclear structure studies, medical treatment |
| X-Rays | Roentgen | High energy electrons hitting heavy targets | 6×10⁻¹⁰ m to 10⁻⁹ m | 5×10¹⁹ Hz to 3×10¹⁷ Hz | 2.4×10³ eV to 1.2×10⁵ eV | Medium penetrating power, similar to gamma rays | Medical diagnosis, crystal structure studies |
| Ultraviolet | Ritter | Ionized gases, sun, spark lamps | 6×10⁻¹⁰ m to 3.8×10⁻⁷ m | 3×10¹⁷ Hz to 5×10¹⁹ Hz | 2×10¹ eV to 3×10² eV | Causes photoelectric effect | Detecting adulteration, water sterilization |
| Visible Light | Newton | Electron transitions in atoms | 3.8×10⁻⁷ m to 7.8×10⁻⁷ m | 8×10¹⁴ Hz to 4×10¹⁴ Hz | 3.2 eV to 1.6 eV | Sensitive to human eye | Vision, molecular structure studies |
| Infrared | Herschel | Molecular vibrations and rotations | 7.8×10⁻⁷ m to 10⁻³ m | 4×10¹⁴ Hz to 3×10¹¹ Hz | 1.6 eV to 10⁻³ eV | Heating effect | Thermal imaging, remote controls |
| Microwaves | Hertz | Klystron tubes, magnetrons | 10⁻³ m to 0.3 m | 3×10¹¹ Hz to 10⁹ Hz | 10⁻³ eV to 10⁻⁶ eV | Reflection, refraction, diffraction | Radar, telecommunications, microwave ovens |
| Radio Waves | Marconi | Oscillating circuits | 0.3 m to few km | 10⁹ Hz to few Hz | 10⁻⁶ eV to ≈0 | Long wavelength, low energy | Communication, broadcasting |
3.2 Radio Wave Subdivisions
| Type | Wavelength Range | Frequency Range | Applications |
|---|---|---|---|
| SHF (Super High Frequency) | 0.01 m to 0.1 m | 3×10¹⁰ Hz to 3×10⁹ Hz | Radar, satellite communication |
| UHF (Ultra High Frequency) | 0.1 m to 1 m | 3×10⁹ Hz to 3×10⁸ Hz | Television communication |
| VHF (Very High Frequency) | 1 m to 10 m | 3×10⁸ Hz to 3×10⁷ Hz | FM radio, television |
| HF (High Frequency) | 10 m to 100 m | 3×10⁷ Hz to 3×10⁶ Hz | Medium distance communication |
| MF (Medium Frequency) | 100 m to 1000 m | 3×10⁶ Hz to 3×10⁵ Hz | AM radio, marine navigation |
| LF (Low Frequency) | 1000 m to 10000 m | 3×10⁵ Hz to 3×10⁴ Hz | Long range communication |
| VLF (Very Low Frequency) | 10000 m to 30000 m | < 3×10⁴ Hz | Long distance communication |