Class 12 Physics · NCERT chapter 8 · 6 topics · free to read
Displacement Current
Maxwell spotted a fatal gap in Ampere's law: it failed for charging capacitors. His fix? A 'displacement current' that flows through empty space wherever the electric field is changing. This single correction predicted electromagnetic waves.
I_d = _0 d _E dt
Ampere's Law Inconsistency
Ampere's circuital law gives contradictory answers when the Amperian loop sits between capacitor plates — Maxwell showed why.
Consider a parallel plate capacitor being charged by a current I . Draw an Amperian loop around the wire. If the surface enclosed is a flat disc cutting the wire, Ampere's law gives B d l = _0 I . But if you stretch the surface to balloon between the plates (where no conduction current flows), it gives B d l = 0 . Same loop, two different answers — that is a contradiction.
Ampere's original law: B d l = _0 I_ enclosed
For a charging capacitor, conduction current I flows in the wire but zero conduction current flows between the plates
The inconsistency arises because the result depends on which surface you pick — the law should give the same B regardless of the surface
This inconsistency ONLY appears in time-varying situations (changing E field between plates)
Displacement Current
Maxwell proposed that a changing electric field between capacitor plates is equivalent to a current. This 'displacement current' restores the consistency of Ampere's law.
Maxwell proposed that a time-varying electric field produces the same magnetic effects as a conduction current. He defined displacement current as:
I_d = _0 d _E dt (NCERT Eq. 8.2)
where _E = E d A is the electric flux through the surface. Between the capacitor plates, E is changing as the capacitor charges, so d _E dt 0 , giving a non-zero displacement current.
I_d = _0 d _E dt — displacement current (unit: Ampere)
Between charging capacitor plates: I_d = I (conduction current in the wire) — they are numerically equal
Displacement current exists wherever E is changing with time, even in empty space
No actual charges move — it is purely due to changing electric field
SI unit of _0 d _E dt → C^2N^ -1 m^ -2 V s^ -1 = A
Ampere-Maxwell Law
Maxwell modified Ampere's law by adding the displacement current term, creating a complete and consistent law.
The corrected form — called the Ampere-Maxwell law — includes both conduction current and displacement current:
B d l = _0(I_c + I_d) = _0 I_c + _0 _0 d _E dt
Now the law gives the same answer regardless of which surface you pick. Through surface S_1 (cutting the wire): I_c = I , I_d = 0 . Through surface S_2 (between plates): I_c = 0 , I_d = I . Both give _0 I .
Total current = I_c + I_d = conduction current + displacement current
Outside capacitors in normal circuits, displacement current is negligible — Ampere's original law works fine
Quick recall
A parallel plate capacitor with plate area A has a time-varying electric field E = E_0 sin(omega t) between its plates. What is the displacement current?
I_d = _0 d _E dt = _0 A dE dt = _0 A E_0 ( t) . The displacement current varies sinusoidally and is maximum when E is changing fastest (at zero crossings).
Maxwell's addition of displacement current was purely theoretical in 1865. It was only confirmed experimentally by Hertz in 1888 when he produced and detected electromagnetic waves — 23 years later!
Electromagnetic Waves
Maxwell's equations predicted that changing electric and magnetic fields can sustain each other and travel through space as waves at the speed of light. Hertz proved it. These waves need no medium — they are self-propagating oscillations of E and B fields.
c = 1 _0 _0 = 3 10^8 m/s
How EM Waves Are Born
Any accelerating charge produces electromagnetic waves. An oscillating charge produces waves of the same frequency as the oscillation.
Maxwell's theory showed that a changing electric field produces a magnetic field (displacement current), and a changing magnetic field produces an electric field (Faraday's law). Together, they create a self-sustaining cycle: E changes B is produced B changes E is produced and so on. This leapfrogging pair propagates through space as an electromagnetic wave.
An accelerating charge is the source of EM waves — a charge at rest or in uniform motion does NOT radiate
An oscillating charge (frequency ) produces EM waves of the same frequency
Static charges produce only E ; steady currents produce only B ; accelerating charges produce both and they radiate outward
Hertz (1888) was the first to experimentally produce and detect EM waves using an oscillating LC circuit
Properties of EM Waves
EM waves are transverse, with E perpendicular to B perpendicular to the direction of propagation. They travel at c in vacuum and need no medium.
For a plane EM wave travelling in the +z direction, the electric field oscillates along x and the magnetic field oscillates along y (or vice versa). The fields are always perpendicular to each other AND to the direction of propagation.
E_x = E_0 (kz - t), B_y = B_0 (kz - t)
Both fields oscillate in phase — they reach their maxima and zeros at the same points in space and time.
EM waves are transverse — E B v
E and B oscillate in phase (same frequency, same phase)
The direction of propagation is given by E B
EM waves do NOT need a medium — they travel through vacuum
All EM waves travel at c = 3 10^8 m/s in vacuum
The ratio of amplitudes: E_0 B_0 = c
Speed of EM Waves
The speed of electromagnetic waves in vacuum is determined entirely by two constants: the permittivity and permeability of free space.
Maxwell derived the speed of EM waves from his equations and found:
c = 1 _0 _0 (NCERT Eq. 8.7)
Substituting _0 = 4 10^ -7 T m/A and _0 = 8.854 10^ -12 C ^2 N ^ -1 m ^ -2 , we get c 3 10^8 m/s — exactly the measured speed of light. This was Maxwell's great triumph: light IS an electromagnetic wave.
In vacuum: c = 1/ _0 _0 3 10^8 m/s
In a medium: v = 1/ = c/n where n is the refractive index
Speed does NOT depend on frequency or wavelength in vacuum (no dispersion)
The relation c = holds for all EM waves
c is the speed for ALL EM waves in vacuum — radio waves, X-rays, gamma rays all travel at the same speed
Quick recall
Do radio waves travel faster or slower than gamma rays in vacuum?
Neither — they travel at the same speed c = 3 10^8 m/s. In vacuum, all EM waves have the same speed regardless of frequency. The difference is only in frequency and wavelength ( c = ).
Energy & Momentum
EM waves carry energy and momentum. The intensity is described by the Poynting vector, and radiation pressure is real enough to push a comet's tail.
EM waves carry energy. The energy density (energy per unit volume) stored in the electric and magnetic fields:
The average energy density: u = 1 2 _0 E_0^2 = B_0^2 2 _0 . Notice: electric and magnetic energy densities are equal on average.
Intensity I = 1 2 c _0 E_0^2 (average power per unit area, unit: W/m ^2 )
Electric and magnetic energy densities are equal on average: u_E = u_B
Momentum carried by EM wave: p = U/c (for complete absorption) or p = 2U/c (for complete reflection)
Radiation pressure on a perfectly absorbing surface: P = I/c
Radiation pressure on a perfectly reflecting surface: P = 2I/c
The Poynting vector S = 1 _0 ( E B ) gives the direction and magnitude of energy flow
S = 1 _0 ( E B ) (Poynting vector, unit: W/m^2)
The fact that EM waves carry momentum was first experimentally verified by Nichols and Hull in 1901, decades after Maxwell's prediction. Today, radiation pressure is being seriously explored for solar sail spacecraft propulsion.
EM Spectrum Overview
The electromagnetic spectrum spans from radio waves (wavelength: kilometres) to gamma rays (wavelength: smaller than an atom). All are the same phenomenon — oscillating E and B fields — differing only in frequency and wavelength.
c = = 3 10^8 m/s
The Seven Regions
The EM spectrum is divided into seven named regions based on frequency/wavelength. Boundaries are not sharp — they overlap.
All EM waves travel at c in vacuum. They differ only in frequency and wavelength , linked by c = . Higher frequency means shorter wavelength and higher energy ( E = h ).
Increasing frequency order: Radio < Microwave < IR < Visible < UV < X-ray < Gamma
Increasing wavelength order: Gamma < X-ray < UV < Visible < IR < Microwave < Radio (exact reverse)
Increasing energy order: Same as frequency — Radio (least) to Gamma (most)
Boundaries between regions are not sharp — they overlap (e.g., soft X-rays and hard UV overlap)
All travel at c = 3 10^8 m/s in vacuum
Frequency & Wavelength Ranges
Each region has a characteristic frequency and wavelength range. You don't need exact boundaries — just orders of magnitude.
Here are the approximate ranges for each region. NEET does NOT expect you to memorize exact cutoffs — just the order of magnitude.
Radio waves
> 0.1 m (can be km long)
Microwaves
0.1 m to 1 mm
Infrared (IR)
1 mm to 700 nm
Visible light
700 nm (red) to 400 nm (violet)
Ultraviolet (UV)
400 nm to 1 nm
X-rays
1 nm to 0.01 nm (10 pm)
Gamma rays
< 0.01 nm (< 10 pm)
Visible light: VIBGYOR — Violet (400 nm) to Red (700 nm)
Frequency range of visible light: 4 10^ 14 Hz to 7.5 10^ 14 Hz
The entire visible spectrum is a tiny sliver: 400–700 nm out of a spectrum spanning 10^ -15 m to 10^ 4 m
Radio waves can have wavelengths of kilometres; gamma rays have wavelengths smaller than an atom
The frequency range of the whole spectrum: 10^4 Hz (radio) to > 10^ 22 Hz (gamma)
Quick recall
Which has a higher frequency: red light or blue light?
Blue light. Within visible light, violet/blue has the shortest wavelength (about 400 nm) and therefore the highest frequency. Red has the longest wavelength (about 700 nm) and lowest frequency. Remember: VIBGYOR goes from high frequency to low frequency.
Common Properties
Despite their vast range, all electromagnetic waves share a set of fundamental properties that follow directly from Maxwell's equations.
All seven types of EM waves are fundamentally the same phenomenon — oscillating electric and magnetic fields. They share these properties:
All are transverse waves ( E B direction of propagation)
All travel at c = 3 10^8 m/s in vacuum
All obey c =
All carry energy and momentum
All can be polarized (since they are transverse)
All are produced by accelerating charges (fundamental source)
All show reflection, refraction, interference, and diffraction
All obey the inverse square law: intensity 1/r^2
NCERT emphasizes: the classification into seven types is based on the method of production and detection, not any fundamental physical difference. If humans could see X-rays, we would perceive them the same way we perceive light — just much higher energy.
Radio, Microwave & Infrared
The three lowest-frequency regions of the EM spectrum. Radio waves carry your FM stations, microwaves heat your food, and infrared is the 'heat radiation' you feel from a bonfire — each with distinct sources, detectors, and applications.
_ radio > _ micro > _ IR > 700 nm
Radio Waves
Radio waves have wavelengths from about 0.1 m to several kilometres. They are produced by oscillating circuits and are the backbone of wireless communication.
Radio waves are produced by accelerating charges in oscillating circuits (LC oscillators, antennas). Hertz first produced them using a spark-gap oscillator in 1888.
Wavelength: > 0.1 m (can be several km)
Frequency: < 3 GHz (sub-bands: AM ~500–1600 kHz, FM ~88–108 MHz, TV bands, shortwave)
Properties: Can diffract around buildings and hills, reflected by ionosphere (AM), travel in straight lines (FM/TV)
AM broadcasting → long wavelength → diffracts around obstacles → long range
FM broadcasting → shorter wavelength → less diffraction → line-of-sight → better audio quality
TV signals → similar to FM range → need tall transmission towers or satellites
Cellular/WiFi → overlap with microwave range (GHz frequencies)
Microwaves
Microwaves have wavelengths from about 1 mm to 0.1 m. They are produced by special vacuum tubes (klystrons, magnetrons) and are used in cooking, radar, and satellite communication.
Microwaves are short-wavelength radio waves. They are produced by klystrons, magnetrons, and Gunn diodes — devices that make electrons oscillate at GHz frequencies.
Wavelength: 1 mm to 0.1 m
Frequency: 3 GHz to 300 GHz
Source: Klystron, magnetron, Gunn diode
Detection: Point-contact diode, crystal detector
Cooking: Water molecules absorb 2.45 GHz microwaves → rotational heating
RADAR (Radio Detection And Ranging) → microwaves reflect off objects → measure distance and speed of aircraft, ships
Satellite communication → microwaves pass through the atmosphere with minimal absorption
WiFi (2.4/5 GHz) and Bluetooth technically use microwaves
Infrared Radiation
Infrared radiation has wavelengths from about 700 nm to 1 mm. Everything warm emits IR. It is produced by hot bodies and molecular vibrations/rotations.
All objects above absolute zero emit infrared radiation. The hotter the object, the more IR it emits and the shorter the peak wavelength (Wien's law). IR is produced by vibrations and rotations of molecules and by hot bodies.
Wavelength: 700 nm to 1 mm
Frequency: 3 10^ 11 Hz to 4 10^ 14 Hz
Source: Hot bodies, molecules (vibrational/rotational transitions), IR LEDs, IR lasers
Detection: Thermopile, bolometer, IR-sensitive photographic film, special semiconductor detectors
Also called thermal radiation or heat radiation
TV/AC remote controls → IR LEDs modulate at ~38 kHz carrier frequency
Night vision → detects IR emitted by warm bodies (humans, animals) in darkness
Greenhouse effect → Earth re-radiates solar energy as IR; greenhouse gases absorb it and re-emit it, trapping heat
Physiotherapy → IR lamps warm deep tissues for pain relief
IR spectroscopy → identifies molecules by their vibrational absorption patterns
Quick recall
Why does a TV remote use infrared instead of visible light?
IR is invisible, so it does not create an annoying flash of light every time you press a button. It is also cheap to produce (simple IR LEDs), confined to short range (so it does not interfere with neighbours), and can be modulated to carry signal data.
Visible, UV & X-rays
Visible light is the tiny window our eyes can detect (400-700 nm). Ultraviolet causes sunburn and kills bacteria. X-rays penetrate flesh but not bone — making them indispensable in medicine. Each has distinct sources and both benefits and dangers.
E = h = hc
Visible Light
Visible light spans 400 nm (violet) to 700 nm (red). It is produced by electron transitions in atoms and is detected by the retina of the eye.
Visible light is the only EM radiation our eyes can detect. It spans a narrow band from about 400 nm (violet) to 700 nm (red). This tiny window is what our entire visual experience is built on.
Wavelength: 400 nm (violet) to 700 nm (red)
Frequency: 4 10^ 14 Hz to 7.5 10^ 14 Hz
Source: Electron transitions in atoms, Sun, incandescent bulbs, LEDs, lasers
Detection: Human eye (retina), photographic film, photodiodes, CCD sensors
VIBGYOR: Violet (400) → Indigo → Blue → Green → Yellow → Orange → Red (700) — increasing wavelength
Ultraviolet (UV)
UV radiation sits just beyond violet light. It has enough energy to damage DNA and cause sunburn, but controlled use kills bacteria and helps produce vitamin D.
Ultraviolet radiation has wavelengths shorter than visible violet light. The Sun is a major natural source, but most solar UV is absorbed by the ozone layer. UV is also produced by special lamps (mercury vapour) and very hot objects.
Wavelength: 400 nm down to about 1 nm
Frequency: 7.5 10^ 14 Hz to 3 10^ 17 Hz
Source: Sun, mercury vapour lamps, arc lamps, very hot stars
Sub-types: UV-A (320–400 nm, least harmful), UV-B (280–320 nm, causes sunburn), UV-C (< 280 nm, germicidal, mostly absorbed by ozone)
Sterilization → UV-C kills bacteria and viruses by damaging their DNA — used in water purifiers, hospital equipment
Vitamin D synthesis → UV-B triggers vitamin D production in human skin
Fluorescence → UV makes certain materials glow (fluorescent lamps, security marks on banknotes)
LASIK eye surgery → UV excimer laser reshapes the cornea
Ozone layer → absorbs most UV-B and all UV-C from the Sun, protecting life on Earth
X-rays
X-rays have wavelengths from about 1 nm to 0.01 nm. They penetrate soft tissue but are absorbed by bone — the basis of medical imaging. Produced by high-energy electron impacts on metal targets.
X-rays are produced when high-energy electrons are decelerated rapidly by hitting a metal target (like tungsten) in an X-ray tube. This process is called Bremsstrahlung (German for 'braking radiation'). Characteristic X-rays are also produced when inner-shell electrons are knocked out and outer electrons fill the vacancy.
Wavelength: ~1 nm to ~0.01 nm (10 pm)
Frequency: 3 10^ 17 Hz to 3 10^ 19 Hz
Source: X-ray tubes (bombarding metal targets with high-speed electrons), synchrotrons
Cancer treatment → high-energy X-rays destroy cancerous cells (radiation therapy)
Gamma Rays & Spectrum Summary
Gamma rays are the most energetic EM waves, born from nuclear reactions and radioactive decay. This concept also brings together the full spectrum in a master comparison — the kind of table that wins you marks in NEET.
E_ = h (highest highest energy)
Gamma Rays
Gamma rays have the shortest wavelengths and highest frequencies in the EM spectrum. They originate from nuclear transitions and are extremely penetrating.
Gamma rays are produced during radioactive decay of nuclei and nuclear reactions (fission, fusion). When a nucleus drops from an excited state to a lower energy state, it emits a gamma-ray photon — analogous to an atom emitting visible/UV light during electronic transitions, but at much higher energy.
Wavelength: < 0.01 nm (< 10 pm) — shorter than the diameter of an atom
Nuclear physics research → studying nuclear structure and reactions
Astronomy → gamma-ray telescopes detect the most violent events in the universe (supernovae, black holes, neutron star mergers)
Most penetrating of all EM waves — can pass through several cm of lead
Stopped effectively only by thick lead or several metres of concrete
Exposure causes ionization damage to living cells — can cause cancer but also treats it (controlled doses)
Inverse square law: intensity drops as 1/r^2 — distance is a safety measure
Master Comparison Table
A single reference table comparing all seven types by wavelength, frequency, source, detection, and key applications. This is the table to memorize for NEET.
Here is the master table. Focus on source and one key application for each — that is what NEET tests most.
Hot bodies, molecular vibrations | Remote controls, night vision, greenhouse effect
Visible
Electron transitions in atoms | Vision, photosynthesis, optical instruments
Ultraviolet
Sun, mercury lamps, very hot bodies | Sterilization, vitamin D, fluorescence, LASIK
X-ray
Electron bombardment of metal target | Medical imaging, CT scan, crystal diffraction
Gamma
Radioactive nuclei, nuclear reactions | Cancer treatment, PET scan, food sterilization
Frequency order: Radio < Micro < IR < Visible < UV < X-ray < Gamma
Wavelength order: Radio > Micro > IR > Visible > UV > X-ray > Gamma (reverse of frequency)
Photon energy order: same as frequency — Gamma photons carry the most energy
Penetrating power: increases with frequency — Gamma most penetrating, Radio least
Ionizing ability: UV, X-ray, and Gamma are ionizing; Radio, Micro, IR, and Visible are non-ionizing
Step 1: Recall the mnemonic — Royal Monkeys In Very Unusual eXpensive Gardens (frequency order)
Step 2: For each type, remember ONE source (how is it made?) and ONE application (what is it used for?)
Step 3: Remember that X-ray vs Gamma is distinguished by ORIGIN (electronic vs nuclear), not wavelength
Step 4: For dangers — UV causes skin cancer, X-rays and Gamma cause DNA damage, microwaves cause heating
Step 5: For atmospheric effects — Radio (AM) bounces off ionosphere, Visible passes through (optical window), IR absorbed by greenhouse gases, UV absorbed by ozone layer
Quick recall
Arrange the following in order of increasing wavelength: gamma rays, visible light, microwaves, X-rays, radio waves.
Gamma < X-rays < Visible < Microwaves < Radio. Just reverse the frequency order from the mnemonic. The one with the highest frequency (gamma) has the shortest wavelength.