Electromagnetic waves tie together everything you have learned about electricity, magnetism and optics into one framework, and in NEET they reliably yield one or two straightforward questions — usually on the ordering of the spectrum, the relations among $E_0$, $B_0$ and $c$, or the idea of displacement current. The concepts are few and mostly formula-based, so this is among the highest return-per-hour topics in the syllabus.
Displacement Current: Patching a Hole in Ampere's Law
Ampere's circuital law, as originally written, says that the line integral of the magnetic field around a closed loop equals $\mu_0$ times the current threading that loop. Maxwell noticed that this statement becomes self-contradictory the moment you apply it to a circuit containing a capacitor that is charging up.
Imagine a parallel-plate capacitor being charged. Take a circular loop encircling the connecting wire. If you choose a flat surface pierced by the wire, the enclosed current is $I$, so the law predicts a non-zero $B$. But you are free to choose a differently shaped surface bounded by the same loop — one that balloons out and passes through the empty gap between the plates. No charge crosses that gap, so the enclosed conduction current is zero, and the law now predicts $B = 0$. Two answers for one physical field is unacceptable.
Maxwell's resolution: while no charges cross the gap, the electric field between the plates is growing, so the electric flux through the gap is changing. He proposed that a changing electric flux behaves, magnetically, exactly like a current. This equivalent current is the displacement current:
$$I_d = \varepsilon_0 \frac{d\Phi_E}{dt}$$
The corrected law (the Ampere–Maxwell law) is
$$\oint \vec{B}\cdot d\vec{l} = \mu_0 (I_c + I_d) = \mu_0 I_c + \mu_0\varepsilon_0\frac{d\Phi_E}{dt}$$
Key points to hold on to:
- For an ideal charging capacitor, the displacement current in the gap exactly equals the conduction current in the wires. The total current $(I_c + I_d)$ is therefore continuous around the whole circuit, with no break at the plates.
- Displacement current requires no charge carriers at all. It exists in vacuum.
- In a steady-state DC circuit nothing changes, $d\Phi_E/dt = 0$, and the law reduces to the familiar Ampere form. Displacement current matters for AC and for transients.
- For a capacitor of plate area $A$ with uniform field $E$, $\Phi_E = EA$, so $I_d = \varepsilon_0 A,(dE/dt)$.
The deep consequence is a symmetry: Faraday showed a changing magnetic field produces an electric field; Maxwell showed a changing electric field produces a magnetic field. Each can regenerate the other, and that mutual regeneration is precisely what allows a disturbance to propagate away from its source as a wave.
Maxwell's Equations and the Birth of the EM Wave
Maxwell summarised all of electromagnetism in four laws. For NEET you need the physical content, not the vector calculus:
- Gauss's law for electricity — electric flux out of a closed surface is $q_{enc}/\varepsilon_0$; electric charges are the sources of $\vec{E}$.
- Gauss's law for magnetism — net magnetic flux through any closed surface is zero; there are no isolated magnetic poles, so magnetic field lines always close on themselves.
- Faraday's law — a changing magnetic flux drives an induced emf, i.e. creates a circulating electric field.
- Ampere–Maxwell law — both conduction current and changing electric flux create a circulating magnetic field.
Solving these together for empty space yields wave equations whose solutions travel at a speed fixed entirely by two electrostatic/magnetostatic constants:
$$c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} \approx 3\times10^8\ \text{m s}^{-1}$$
Plugging in $\mu_0 = 4\pi\times10^{-7}$ T m A⁻¹ and $\varepsilon_0 = 8.85\times10^{-12}$ C² N⁻¹ m⁻² gives the measured speed of light. This numerical coincidence was the argument that light is an electromagnetic wave.
What produces such waves? An accelerating (or oscillating) charge. A charge at rest gives only a static electric field; a charge in uniform motion gives steady $\vec{E}$ and $\vec{B}$ fields; only acceleration radiates. In an LC oscillator or antenna, charges oscillate with frequency $\nu$ and radiate EM waves of that same frequency. Hertz demonstrated this experimentally with spark-gap oscillators; Bose and Marconi extended it to shorter and longer wavelengths respectively.
Nature and Properties of Electromagnetic Waves
A plane electromagnetic wave travelling along the $x$-axis can be written as
$$E_y = E_0 \sin(kx - \omega t), \qquad B_z = B_0 \sin(kx - \omega t)$$
Note carefully what this says: $\vec{E}$ oscillates along $y$, $\vec{B}$ along $z$, and propagation is along $x$. The essential properties:
- Transverse: both $\vec{E}$ and $\vec{B}$ are perpendicular to the direction of propagation.
- Mutually perpendicular: $\vec{E} \perp \vec{B}$, and the direction of propagation is along $\vec{E}\times\vec{B}$.
- In phase: both fields reach their maxima and zeros at the same place and time.
- Amplitude relation: $\dfrac{E_0}{B_0} = c$, and at every instant $E = cB$. Since $c$ is large, the numerical value of $B$ is always tiny compared with $E$ in SI units — this does not mean the magnetic part is unimportant.
- No medium needed: they travel through vacuum. This is what distinguishes them from sound and other mechanical waves.
- Uncharged: EM waves are not deflected by external electric or magnetic fields.
- Speed in a medium: $v = \dfrac{1}{\sqrt{\mu\varepsilon}} = \dfrac{c}{n}$, where $n$ is the refractive index. On entering a medium the frequency stays fixed (it is set by the source) while wavelength and speed decrease.
- $c = \nu\lambda$ and $\omega = ck$ hold, with $\omega = 2\pi\nu$, $k = 2\pi/\lambda$.
Energy, Intensity and Momentum
An EM wave carries energy stored in both fields. The energy densities are
$$u_E = \tfrac{1}{2}\varepsilon_0 E^2, \qquad u_B = \frac{B^2}{2\mu_0}$$
Using $E = cB$ and $c^2 = 1/\mu_0\varepsilon_0$, one finds $u_E = u_B$: the energy is shared equally between the electric and magnetic fields. This is a favourite one-line question. The total average energy density, using $\langle \sin^2\rangle = 1/2$, is
$$\langle u \rangle = \tfrac{1}{2}\varepsilon_0 E_0^2 \cdot \tfrac{1}{2} \times 2 = \tfrac{1}{2}\varepsilon_0 E_{0}^{2}\ \text{(total)} ;=; \varepsilon_0 E_{rms}^2$$
with $E_{rms} = E_0/\sqrt{2}$. Intensity — power per unit area — is the energy density carried forward at speed $c$:
$$I = \langle u \rangle c = \tfrac{1}{2}\varepsilon_0 E_0^2 c$$
For a point source radiating power $P$ isotropically, $I = P/4\pi r^2$, which lets you extract $E_0$ and $B_0$ at a given distance — a standard numerical.
EM waves also carry momentum. If a wave delivers energy $U$ to a surface that completely absorbs it, the momentum transferred is
$$p = \frac{U}{c}$$
and the resulting radiation pressure is $I/c$ for a perfect absorber (and $2I/c$ for a perfect reflector, since the momentum reverses). Radiation pressure is tiny for everyday light but is the principle behind solar sails and shapes comet tails.
The Electromagnetic Spectrum
All EM waves are physically the same kind of entity; they differ only in frequency (and hence wavelength). In vacuum every one of them travels at $c$. The classification, in order of increasing frequency / decreasing wavelength:
- Radio waves ($\lambda >$ ~0.1 m, $\nu$ from a few hundred kHz to ~10⁹ Hz) — produced by accelerated charges in antennas. Used in radio, TV broadcasting, and cellular communication. AM band ~530 kHz–1710 kHz; TV and FM in the tens to hundreds of MHz.
- Microwaves (~10⁹–10¹¹ Hz, mm to cm) — from klystrons, magnetrons, Gunn diodes. Used in RADAR, satellite links and microwave ovens, which work by resonantly agitating water molecules (frequency matched to the rotational/vibrational response of water) so that food heats from within.
- Infrared (~10¹¹–4×10¹⁴ Hz, just beyond red) — emitted by all warm bodies; called heat waves. Absorbed by water and CO₂ in the atmosphere (greenhouse effect keeps the Earth warm). Used in remote controls, night vision, physiotherapy, and long-distance photography through haze.
- Visible light (~4×10¹⁴ to 7×10¹⁴ Hz, 700 nm down to 400 nm) — the narrow band the human retina detects; VIBGYOR from shortest to longest wavelength reversed.
- Ultraviolet (~7×10¹⁴–10¹⁷ Hz, 400 nm to 0.6 nm) — from the Sun and arc welding; causes sunburn and damages the eye. Mostly filtered by the stratospheric ozone layer. Used to sterilise water and surgical instruments, and in UV-based eye surgery (LASIK).
- X-rays (~10¹⁶–10¹⁹ Hz, 10 nm to 10⁻⁴ nm) — produced when fast electrons decelerate on striking a metal target. Used in medical imaging and radiotherapy; overexposure damages living tissue.
- Gamma rays ($\nu > $ ~10¹⁸–10¹⁹ Hz) — emitted in nuclear transitions and radioactive decay. Highest energy; used to destroy cancer cells and to sterilise medical supplies.
The bands overlap at their edges and the boundaries are conventions, not sharp physical lines. Two useful mnemonic anchors: the order is Radio–Micro–IR–Visible–UV–X–Gamma, and photon energy $E = h\nu$ increases along the same direction, which is why the right-hand end of the list is the dangerous, ionising end.
Common Mistakes and Exam Traps
Thinking displacement current involves moving charge. It does not. It is a changing electric flux dressed up as a current so that Ampere's law works. Also remember that no actual charge crosses the gap between the plates — there is no drift velocity and no ohmic heating associated with $I_d$ there; it only reproduces the magnetic effect a real current would have.
Assuming $E_0/B_0 = c$ means the electric part matters more than the magnetic part. The large numerical gap between $E_0$ and $B_0$ in SI units is purely an artefact of unit choice; the energy carried by the two fields is exactly equal ($u_E = u_B$ at every instant), so neither field dominates the wave physically.
Placing $\vec{E}$, $\vec{B}$ and the direction of travel in the wrong relative orientation. All three are mutually perpendicular, with $\vec{E}\times\vec{B}$ pointing along the direction of propagation — it is easy to sketch $\vec{E}$ and $\vec{B}$ oscillating in the same plane, or to reverse which vector the cross product should give.
Misordering the spectrum or its uses. A common trap swaps microwaves and infrared, or forgets that frequency (not wavelength) rises in the same direction as photon energy — the order Radio < Micro < IR < Visible < UV < X-ray < Gamma runs from low to high frequency and energy, and it is the high-frequency end (UV, X-ray, gamma) that is ionising and biologically dangerous, not the radio end.