1. The Concept of Displacement Current
Before Maxwell, Ampere’s Circuital Law was considered incomplete. Maxwell noticed that in a charging capacitor, a magnetic field existed even in the gap where no actual electrons were flowing.
- Displacement Current (Id): It is the current that arises due to the change in electric flux with time.
- Formula: Id = ε₀ (dΦE / dt)
- Modified Ampere-Maxwell Law: ∮ B · dl = μ₀ (Ic + Id)
Rich Insight: This discovery proved that a changing electric field produces a magnetic field, just as a changing magnetic field produces an electric field (Faraday’s Law).
2. Maxwell’s Equations
Maxwell summarized all of electromagnetism into four fundamental equations that govern every electrical and magnetic phenomenon:
- Gauss’s Law for Electricity: ∮ E · dA = q / ε₀
- Gauss’s Law for Magnetism: ∮ B · dA = 0
- Faraday’s Law: ∮ E · dl = -(dΦB / dt)
- Ampere-Maxwell Law: ∮ B · dl = μ₀ Ic + μ₀ ε₀ (dΦE / dt)
3. Characteristics of EM Waves
EM Waves are produced by accelerated charges. Unlike sound waves, they do not require a medium (like air or water) to travel.
- Transverse Nature: The Electric field (E), Magnetic field (B), and the direction of propagation are all mutually perpendicular to each other.
- Speed: In a vacuum, they travel at the speed of light: c = 3 × 10⁸ m/s.
- Energy: They carry energy and momentum. The energy is shared equally between the electric and magnetic fields.
- Constant Relation: The ratio of the amplitudes is always constant: E₀ / B₀ = c.
4. The Electromagnetic Spectrum
Students often get confused by the ranges. Use this table to memorize the order and primary uses.
| Wave Type | Wavelength Range | Source | Primary Use |
| Radio Waves | > 0.1 m | Accelerated electrons | Radio, TV, Mobile Comms |
| Microwaves | 1 mm to 0.1 m | Magnetron valves | Radar, Microwave Ovens |
| Infrared | 700 nm to 1 mm | Hot bodies | Remote controls, Night vision |
| Visible Light | 400 nm to 700 nm | Atomic electrons | Human vision |
| Ultraviolet | 1 nm to 400 nm | Sun, UV lamps | Water purification, LASIK |
| X-Rays | 0.01 nm to 10 nm | High energy electrons | Medical imaging, Security |
| Gamma Rays | < 10⁻¹² m | Radioactive nuclei | Cancer treatment |
🚀 Competitive Corner: NEET & JEE Focus
- Intensity: Intensity (I) = Average Energy Density × c.
- Radiation Pressure: When EM waves strike a surface, they exert pressure. P = I / c.
- Frequency Order: Always remember the order of increasing frequency: Radio < Micro < IR < Visible < UV < X-ray < Gamma.
- Mnemonic: “Red Monkeys Invade Very Unusual X-ray Gardens.”
💡 “Rich” Study Tips for Mobotes Students
Energy Equality: Even though the Electric field is much stronger in magnitude than the Magnetic field (by a factor of 3 × 10⁸), the energy they carry is exactly the same.
The Capacitor Logic: In many board exams, they ask about the current inside a capacitor. Remember: The conduction current (Ic) is zero in the gap, and only displacement current (Id) exists there.