Electromagnetic waves are transverse waves produced by oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation. Unlike mechanical waves, they do not require a material medium and travel through vacuum at the speed of light, c = 3 x 108 m/s.
Key Concepts and Definitions
Displacement Current: Maxwell introduced the concept of displacement current to complete Ampere's law. When a capacitor is being charged, no conduction current flows between the plates, yet a changing electric field exists. This changing electric field produces a displacement current Id = epsilon0 x (d phiE / dt), where phiE is the electric flux.
- 1.Maxwell's Equations (conceptual form):
- 2.Gauss's Law for electricity: electric field lines originate from charges.
- 3.Gauss's Law for magnetism: magnetic monopoles do not exist.
- 4.Faraday's Law: a changing magnetic field produces an electric field.
- 5.Ampere-Maxwell Law: a changing electric field (displacement current) produces a magnetic field.
- Properties of EM Waves:
- Transverse in nature; E and B are mutually perpendicular and perpendicular to velocity.
- Travel at speed c = 1 / √(mu0 x epsilon0) = 3 x 108 m/s in vacuum.
- Carry energy and momentum; no charge, no mass.
- Can be polarised.
- Obey superposition principle.
Energy carried: The energy is equally distributed between E and B fields.
Intensity I = (1/2) epsilon0 c E02 = (c B02) / (2 mu0)
Momentum: p = U/c, where U is the energy carried.
Electromagnetic Spectrum
| Radiation | Wavelength Range | Production | Uses |
|---|---|---|---|
| Radio waves | > 0.1 m | Oscillating circuits | Communication |
| Microwaves | 1 mm – 0.1 m | Klystron/Magnetron | RADAR, cooking |
| Infrared | 700 nm – 1 mm | Hot bodies | Heating, remote sensing |
| Visible | 400 – 700 nm | Electron transitions | Vision |
| Ultraviolet | 1 nm – 400 nm | Sun, UV lamps | Sterilisation |
| X-rays | 0.001 – 10 nm | X-ray tubes | Medical imaging |
| Gamma rays | < 0.001 nm | Nuclear decay | Cancer treatment |
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A capacitor is being charged by a time-varying current of 2 A. Find the displacement current between the plates.
The displacement current equals the conduction current in steady state: Id = 2 A. This follows from the Maxwell-Ampere law requiring continuity.
The electric field amplitude of an EM wave is E0 = 120 N/C. Find B0.
B0 = E0 / c = 120 / (3 x 108) = 4 x 10-7 T
Find the intensity of an EM wave with E0 = 50 N/C. (epsilon0 = 8.85 x 10-12 C2/Nm2)
I = (1/2) epsilon0 c E02 = 0.5 x 8.85 x 10-12 x 3 x 108 x 2500 = 3.32 W/m2
The wavelength of a microwave is 5 cm. Find its frequency.
f = c / lambda = (3 x 108) / (5 x 10-2) = 6 x 109 Hz = 6 GHz
An EM wave has frequency 1015 Hz. Identify the region of the EM spectrum and find wavelength.
lambda = c/f = (3 x 108) / (1015) = 3 x 10-7 m = 300 nm. This lies in the ultraviolet region.
Momentum delivered by an EM wave pulse of energy 3 x 10-3 J falling on a surface.
p = U/c = (3 x 10-3) / (3 x 108) = 10-11 kg m/s
A parallel plate capacitor has plates of area 100 cm2, separation 2 mm, and voltage changing at 106 V/s. Find displacement current.
d phiE / dt = A x (dE/dt) = A x (1/d) x (dV/dt) = (100 x 10-4) x (1/0.002) x 106 = 5 x 106 V m/s... Wait recalculate: (dE/dt) = (dV/dt)/d = 106/0.002 = 5 x 108 V/m/s. d phiE/dt = A x dE/dt = 100 x 10-4 x 5 x 108 = 5 x 106 Vm/s. Id = epsilon0 x 5 x 106 = 8.85 x 10-12 x 5 x 106 = 4.4 x 10-5 A.
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Common mistakes
- Confusing displacement current with conduction current — they are equal in value but displacement current does not involve charge flow.
- Mixing up E0 and B0 units — E in N/C, B in Tesla.
- Thinking EM waves cannot travel through vacuum — they can and do.
Summary
Maxwell unified electricity and magnetism through displacement current. EM waves are self-sustaining oscillations of E and B fields travelling at c. The EM spectrum from radio waves to gamma rays varies in wavelength and has distinct applications in daily life.