Electromagnetic Waves — NEET Notes

Maxwell's correction — the missing piece

In Class 12 Physics, three great laws describe the electric and magnetic fields produced by sources. Gauss's law tells you that electric charges produce electric flux. Ampère's circuital law tells you that conduction currents produce magnetic fields. Faraday's law tells you that a magnetic field changing with time gives rise to an electric field. James Clerk Maxwell, working in the 1860s, noticed that the system was almost — but not quite — symmetric. If a changing magnetic field produced an electric field, did a changing electric field not produce a magnetic field? Ampère's law as it stood made no such claim, and Maxwell soon discovered that the law was actually internally inconsistent in a perfectly ordinary setting: a capacitor being charged.

The setting is simple. A parallel-plate capacitor sits in a circuit carrying a time-dependent current i(t). Outside the capacitor, the wire carries this current. Between the plates of the capacitor, there is no wire and no conduction — only a growing electric field. Ampère's circuital law, applied along a loop of radius r surrounding the wire just outside the capacitor, gives a clean answer: B(2πr) = μ₀i. But Ampère's law involves a surface bounded by the loop — and any surface will do. Choose the obvious flat disc, pierced by the wire, and you get the answer above. Choose a "pot-shaped" surface that dips between the plates of the capacitor instead, and not a single conduction electron crosses the surface. The right-hand side becomes zero. The same loop, the same point P, but two different answers. The law had to be incomplete.

Maxwell's greatest achievement was the unification of the laws of electricity and magnetism — discovered by Coulomb, Oersted, Ampère, and Faraday — into a consistent set of equations.

NCERT, Class XII Physics, Chapter 8

What crosses the pot-shaped surface that dips between the plates? Not charge, but electric field. The plates carry a charge Q that changes with time; the electric flux Φ_E between them changes in lockstep. Maxwell argued that this changing electric flux must itself act as a source of magnetic field — exactly as a conduction current does. He named the missing term the displacement current.

Displacement current

The reasoning is short. For a parallel-plate capacitor with plate area A and charge Q, the electric field between the plates (from Gauss's law) is E = (Q/A)/ε₀. The flux through the area A is therefore Φ_E = E · A = Q/ε₀. If Q changes with time, so does the flux. Differentiate:

Note that the dimensions work: ε₀ has units that exactly convert the rate of change of flux into amperes. NEET 2021 tested this directly — a capacitor connected to V = V₀ sin ωt has displacement current i_d = C(dV/dt) = V₀ωC cos ωt, a 90° phase shift from the voltage.

The Ampère–Maxwell law

The generalised law that Maxwell produced reads

∮ B·dl = μ₀ ( i_c + ε₀ dΦ_E/dt )

Ampère–Maxwell law — total current is conduction plus displacement

The conduction current i_c is what flows through wires; the displacement current ε₀ dΦ_E/dt is what flows, in effect, wherever the electric field changes with time. Both contribute to the magnetic field. In a charging capacitor, they take turns: outside the plates only conduction current is present, inside the plates only displacement current. The total is the same and continuous across the gap — which is why a magnetic field measured just inside the capacitor matches one measured just outside.

Maxwell's equations — the unified set

Once Ampère's law was repaired, electromagnetism collapsed into a beautifully symmetric quartet of equations. NCERT states them in integral form, in vacuum:

Together with the Lorentz force F = q(E + v × B), these four statements describe every classical electromagnetic phenomenon — and predict, without any further assumption, the existence of waves.

How are electromagnetic waves produced?

Maxwell's equations have a clean and surprising consequence. Faraday's law says that a changing magnetic field produces an electric field; the Ampère–Maxwell law says that a changing electric field produces a magnetic field. Stitch these together — let one feed the other — and you have a self-sustaining oscillation that travels through empty space. The catch is the source: only a charge that is accelerating can launch this cascade.

NCERT spells out the qualitative reasoning. A stationary charge produces only an electrostatic field — no time-variation, no magnetic field at all. A charge in uniform motion (a steady current) produces a magnetic field, but it does not vary, so it cannot induce an electric field, and the wave cycle never starts. An accelerating charge — for instance, one oscillating about a mean position — produces a time-varying electric field, which produces a time-varying magnetic field, which produces a further time-varying electric field, and so on. The disturbance peels away from the source and propagates outwards at the speed of light. NEET 2016 tested this with one of the most direct questions imaginable: which one can be used to produce a propagating electromagnetic wave? The answer was, of course, an accelerating charge.

The energy radiated by an EM wave comes at the expense of the kinetic energy of the accelerating charge. This is why a radiating dipole, left to itself, eventually stops oscillating: it gives its energy to the field. It also explains why the frequency of an EM wave equals the frequency of oscillation of its source — and why we cannot generate visible light by simply oscillating current in a wire. Visible light has a frequency near 6 × 10¹⁴ Hz, far beyond what any electronic circuit can drive. Heinrich Hertz produced the first laboratory radio waves in 1887; Jagadish Chandra Bose followed in Calcutta with microwaves a few years later.

Nature of electromagnetic waves

An electromagnetic wave is transverse. The electric field E, the magnetic field B, and the direction of propagation k̂ are mutually perpendicular. NCERT shows the standard picture: a plane wave moving along the z-axis, with

E_x = E₀ sin(kz − ωt),  B_y = B₀ sin(kz − ωt)

A linearly polarised plane EM wave

The two fields oscillate in phase — they reach peaks and zeros together — and they are tied together in both magnitude and direction. The relations that NEET tests over and over are these:

The direction rule is the second great PYQ favourite. The vector E × B always points in the direction the wave is travelling. If you know E and the direction of propagation, you can recover B. NEET 2018 gave E along +ĵ with propagation along +î and asked for B: the answer must satisfy î = ĵ × B̂, which forces B along +k̂. NEET 2021 gave four candidate (E, B) pairs and asked which propagated along the x-axis — only the pair whose cross product equalled a positive multiple of î survived.

Speed of EM waves — in vacuum and in media

Maxwell's equations, when combined for empty space, force the propagation speed to be c = 1/√(μ₀ε₀). Plugging in the standard values — μ₀ = 4π × 10⁻⁷ T·m/A and ε₀ = 8.854 × 10⁻¹² C²/(N·m²) — gives c ≈ 2.998 × 10⁸ m/s, exactly the speed of light measured by Fizeau and Foucault from optical experiments decades earlier. The numerical agreement is the entire reason Maxwell concluded that light is an electromagnetic wave. This was the unification of three disparate fields — electricity, magnetism, and optics — into one theory.

Inside a material medium, the vacuum constants μ₀ and ε₀ are replaced by μ = μ₀μ_r and ε = ε₀ε_r, where μ_r and ε_r are the relative permeability and relative permittivity. The wave speed becomes

v = 1/√(μ ε) = c/√(μ_r ε_r)

Speed of EM wave in a material medium

This is precisely the question NEET 2022 asked. Light always slows down on entering a denser medium because the product μ_rε_r exceeds unity. The factor √(μ_rε_r) is in fact the refractive index n of the medium relative to vacuum — a deep connection between electromagnetism (Chapter 8) and ray optics (Chapter 9) that NCERT flags explicitly.

Energy, intensity, and momentum

An electromagnetic wave carries energy — that is what allows sunlight to warm the Earth and a transmitter to deliver a radio signal to a distant receiver. The energy is stored in both the electric and the magnetic fields, in equal measure. The instantaneous energy densities are u_E = ½ε₀E² for the electric field and u_B = B²/(2μ₀) for the magnetic field. Substituting E = cB and c = 1/√(μ₀ε₀) shows immediately that u_E = u_B — the two halves are exactly balanced. NEET 2020 made this its full question: the ratio of contributions to intensity from E and B is 1 : 1.

The total time-averaged intensity (energy per area per second) is

The wave also carries linear momentum. If energy U is delivered to a perfectly absorbing surface, the momentum delivered is

p = U / c

Linear momentum of an EM wave (perfect absorption)

For a perfectly reflecting surface, the momentum delivered doubles to 2U/c, because the wave's momentum reverses. This is the principle behind radiation pressure — feeble for sunlight on a leaf, but enough to push light-sails in proposed deep-space propulsion. For NEET, the formula p = U/c is what matters: every joule of EM energy carries 1/c kg·m/s of momentum.

The electromagnetic spectrum — seven regions

Once Maxwell's theory had established that all electromagnetic waves travel at c in vacuum and obey the same equations, the classification of EM radiation became a matter of frequency (or equivalently, wavelength, since c = νλ). The spectrum stretches from gamma rays at frequencies above 10¹⁹ Hz (wavelengths shorter than 10⁻¹³ m) all the way down to radio waves below a megahertz (wavelengths of hundreds of metres). The boundaries between the seven traditional regions are not sharp — they overlap — and the names reflect history rather than physics. What changes from one region to the next is the source that produces the radiation and the way matter interacts with it.

The biological effects scale with the photon energy E = hν. Gamma rays, X-rays, and short-wavelength UV are ionising: each photon carries enough energy to knock electrons out of atoms, breaking chemical bonds and damaging DNA. Visible light and longer wavelengths are non-ionising; they can heat tissue (infrared, microwaves) but cannot ionise it directly. This is why a chest X-ray dose is regulated and why standing in front of a microwave oven is not advisable, but reading by lamplight is harmless.

Visible vs ultraviolet — boundary that matters

The boundary between visible light and ultraviolet sits at roughly 400 nm — the violet end of what the human eye can detect. On either side, the physics is identical, but the biological consequences diverge sharply. NEET likes to test this boundary directly: where does sunburn come from? Which band drives LASIK surgery? Why does ordinary window glass tan your face less than open sky?