Electromagnetic Waves
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Direct answer
Maxwell's insight was that a changing electric field generates a changing magnetic field and vice versa, so the two sustain each other and travel together as a transverse wave at c = 1/sqrt(μ0ε0) = 3 × 10^8 m/s in vacuum — light being one member of the family. The displacement-current repair to Ampere's law is the theoretical hinge, and the spectrum from radio to gamma, with its named bands and uses, is what NEET-UG actually examines.
What you must remember
- Displacement current I_d = ε0 dΦ_E/dt: a changing electric field is equivalent to a current, patching Ampere's law so the field between capacitor plates stays consistent; total current = conduction + displacement.
- Wave shape: E ⊥ B ⊥ direction of propagation; E and B oscillate in phase with E0/B0 = c; the waves are transverse and need no medium.
- Energy divides equally between the fields; intensity I = (1/2)ε0 E0^2 c; momentum carried is U/c, so radiation pressure is I/c on a perfect absorber and 2I/c on a perfect reflector.
- Spectrum by wavelength (NCERT values): radio above 0.1 m; microwaves 0.1 m to 1 mm; infrared 1 mm to 700 nm; visible 700 to 400 nm; ultraviolet 400 to 1 nm; X-rays 1 nm to 10^-3 nm; gamma below 10^-3 nm.
- Band uses: radio and TV broadcast; radar and microwave ovens; infrared remotes, night vision and physiotherapy; UV sterilisation and fluorescent lamps; X-rays imaging; gamma rays cancer therapy.
- The ozone layer absorbs harmful solar UV; greenhouse gases (CO2 and water vapour) transmit visible light but trap outgoing infrared — the greenhouse effect.
- Hertz produced and detected electromagnetic waves in 1887, confirming Maxwell's 1865 prediction; microwaves were studied by Jagadish Chandra Bose, whose millimetre-wave work is a matter of national pride in Indian physics courses.
Why the capacitor forced Maxwell's hand
Charge a capacitor through a wire. Ampere's law, in its original form, relates the magnetic field around any loop to the current piercing the surface the loop bounds — but choose the surface to pass between the plates, where no conduction current flows, and the law returns a different field for the same loop. Contradiction. Maxwell's repair: the changing electric field between the plates is itself a current, I_d = ε0 dΦ_E/dt, numerically equal to the conduction current in the wire, so every surface spanning the loop is pierced by the same total current and the magnetic field becomes well-defined again. The repair is not cosmetic — it is a new statement that a changing E field sources a B field, the mirror of Faraday's changing-B-sources-E. Put the two together and fields can propagate: an E that changes makes a B that changes makes an E... and Maxwell computed the speed of this self-sustening ripple as 1/sqrt(μ0ε0) = 3 × 10^8 m/s, the measured speed of light. Hertz's sparks twenty-two years later, and Bose's millimetre waves after, closed the case.
Where students slip
The ordering question — arrange the bands by wavelength or by frequency — flips the answer: wavelength order radio to gamma is descending, frequency order is ascending, and the exam deliberately mixes the two phrasings. Second, E0/B0 = c, so the magnetic field amplitude in SI units is tiny compared with E0; students who invert the ratio lose the check the formula provides. Third, displacement current is not carried by charges and exists even in vacuum — "no current can flow through empty space" is false in Maxwell's sense, and assertion-reason questions probe precisely this. Fourth, X-rays and gamma rays overlap in the table and are distinguished by origin, not by wavelength: fast-electron deceleration for X-rays, nuclear transitions for gamma. Fifth, the greenhouse mechanism: incoming visible passes the atmosphere, the re-radiated infrared cannot — students who say CO2 blocks sunlight have the direction backwards, and the ozone question is the mirror trap (it filters UV, not IR).
Frequently asked questions
What is displacement current?
ε0 times the rate of change of electric flux — a changing electric field acting as a current, which Maxwell added to Ampere's law to keep the magnetic field between capacitor plates consistent with the field around the feeding wire.
What is the ratio of electric to magnetic field amplitudes in an electromagnetic wave?
E0/B0 = c, the speed of light; in vacuum this holds at every instant and place, with E, B and propagation mutually perpendicular.
Which band of solar radiation does the ozone layer absorb?
Harmful ultraviolet; the greenhouse gases CO2 and water vapour, by contrast, absorb outgoing infrared, which is a different layer and a different mechanism.
Arrange the spectrum in increasing frequency.
Radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays — the exact reverse of the wavelength ordering, which is how the question is usually disguised.
What pressure does radiation exert on a perfect absorber?
P = I/c, where I is the intensity; a perfect reflector experiences double, 2I/c, because the momentum of the light reverses on reflection.