Electromagnetic Waves
Maxwell's equations qualitatively, EM spectrum, properties of EM waves.
Properties of EM waves
Speed = 1/√(μ₀ε₀), transverse, energy carriers.
Maxwell's equations (1861-65) unified electricity and magnetism. The four equations qualitatively:
- Gauss's law for E: electric flux through closed surface = enclosed charge / ε₀.
- Gauss's law for B: magnetic flux through closed surface = 0 (no magnetic monopoles).
- Faraday's law: changing B → induced E.
- Ampere-Maxwell law: current AND changing E → B.
The last two say: a changing E creates B, and a changing B creates E. Together, they propagate as a wave even in vacuum. This is the EM wave.
Properties of EM waves:
- Speed in vacuum: c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s. (Speed of light is a consequence of Maxwell's equations.)
- Transverse: E and B oscillate perpendicular to direction of propagation AND to each other.
- In phase: E and B reach peaks at the same time.
- Magnitude relation: E = c · B (so E is much larger than B by SI units).
- Carry energy and momentum. Pressure exerted on absorbing surface = I/c (intensity / speed of light).
- No medium required. Light travels through vacuum (unlike sound).
- Can be polarized (transverse — vibration in specific direction).
Energy density:
- Electric: u_E = ½ ε₀ E²
- Magnetic: u_B = B² / (2μ₀)
- u_E = u_B in a vacuum EM wave (energy is split equally).
Intensity: I = (1/2) ε₀ c E₀² (E₀ = peak amplitude).
Electromagnetic spectrum — ordered by frequency (or wavelength):
| Band | Wavelength | Frequency | Source / use |
|---|---|---|---|
| Radio | > 1 m | < 300 MHz | Broadcast, AM/FM, mobile |
| Microwave | 1 mm to 1 m | 300 MHz to 300 GHz | RADAR, microwave oven, Wi-Fi, 5G |
| Infrared | 700 nm to 1 mm | 4×10¹¹ to 4×10¹⁴ Hz | Heat, TV remote, IR cameras |
| Visible | 400 nm to 700 nm | 4×10¹⁴ to 7.5×10¹⁴ Hz | Light we see (VIBGYOR) |
| Ultraviolet | 10 nm to 400 nm | up to 3×10¹⁶ Hz | Sun, sterilization, sunburn |
| X-rays | 0.01 nm to 10 nm | up to 3×10¹⁹ Hz | Medical imaging, crystallography |
| Gamma | < 0.01 nm | > 3×10¹⁹ Hz | Nuclear decay, cosmic rays |
Visible spectrum (VIBGYOR): Violet 400nm → Indigo → Blue → Green → Yellow → Orange → Red 700nm.
Higher frequency → higher energy per photon (E = hf). UV/X/gamma are ionizing (can break molecular bonds).
Generation of EM waves: accelerating charges. Examples:
- Antenna with AC current → radio waves.
- Hot bodies → blackbody radiation (mostly IR).
- Electron transitions in atoms → visible/UV.
- Nuclear transitions → gamma.
- Bremsstrahlung (deceleration of electrons) → X-rays.
Worked example. Wavelength of a microwave at 2.4 GHz (Wi-Fi)?
λ = c/f = (3 × 10⁸) / (2.4 × 10⁹) = 0.125 m = 12.5 cm.
This is why kitchen microwaves operate at 2.45 GHz — wavelength matches the depth where water molecules absorb the field efficiently, heating food uniformly.
EM spectrum
Radio → gamma, characteristic wavelengths and uses.
Maxwell's equations (1861-65) unified electricity and magnetism. The four equations qualitatively:
- Gauss's law for E: electric flux through closed surface = enclosed charge / ε₀.
- Gauss's law for B: magnetic flux through closed surface = 0 (no magnetic monopoles).
- Faraday's law: changing B → induced E.
- Ampere-Maxwell law: current AND changing E → B.
The last two say: a changing E creates B, and a changing B creates E. Together, they propagate as a wave even in vacuum. This is the EM wave.
Properties of EM waves:
- Speed in vacuum: c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s. (Speed of light is a consequence of Maxwell's equations.)
- Transverse: E and B oscillate perpendicular to direction of propagation AND to each other.
- In phase: E and B reach peaks at the same time.
- Magnitude relation: E = c · B (so E is much larger than B by SI units).
- Carry energy and momentum. Pressure exerted on absorbing surface = I/c (intensity / speed of light).
- No medium required. Light travels through vacuum (unlike sound).
- Can be polarized (transverse — vibration in specific direction).
Energy density:
- Electric: u_E = ½ ε₀ E²
- Magnetic: u_B = B² / (2μ₀)
- u_E = u_B in a vacuum EM wave (energy is split equally).
Intensity: I = (1/2) ε₀ c E₀² (E₀ = peak amplitude).
Electromagnetic spectrum — ordered by frequency (or wavelength):
| Band | Wavelength | Frequency | Source / use |
|---|---|---|---|
| Radio | > 1 m | < 300 MHz | Broadcast, AM/FM, mobile |
| Microwave | 1 mm to 1 m | 300 MHz to 300 GHz | RADAR, microwave oven, Wi-Fi, 5G |
| Infrared | 700 nm to 1 mm | 4×10¹¹ to 4×10¹⁴ Hz | Heat, TV remote, IR cameras |
| Visible | 400 nm to 700 nm | 4×10¹⁴ to 7.5×10¹⁴ Hz | Light we see (VIBGYOR) |
| Ultraviolet | 10 nm to 400 nm | up to 3×10¹⁶ Hz | Sun, sterilization, sunburn |
| X-rays | 0.01 nm to 10 nm | up to 3×10¹⁹ Hz | Medical imaging, crystallography |
| Gamma | < 0.01 nm | > 3×10¹⁹ Hz | Nuclear decay, cosmic rays |
Visible spectrum (VIBGYOR): Violet 400nm → Indigo → Blue → Green → Yellow → Orange → Red 700nm.
Higher frequency → higher energy per photon (E = hf). UV/X/gamma are ionizing (can break molecular bonds).
Generation of EM waves: accelerating charges. Examples:
- Antenna with AC current → radio waves.
- Hot bodies → blackbody radiation (mostly IR).
- Electron transitions in atoms → visible/UV.
- Nuclear transitions → gamma.
- Bremsstrahlung (deceleration of electrons) → X-rays.
Worked example. Wavelength of a microwave at 2.4 GHz (Wi-Fi)?
λ = c/f = (3 × 10⁸) / (2.4 × 10⁹) = 0.125 m = 12.5 cm.
This is why kitchen microwaves operate at 2.45 GHz — wavelength matches the depth where water molecules absorb the field efficiently, heating food uniformly.