PhysicsNCERT Class 12
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Electromagnetic Waves Notes

Study Notes

4 Topics19 Formulas28 PYQs30 Key Points

Topics

4
1

Chapter Overview

Overview

Electromagnetic Waves connects electricity, magnetism and light through Maxwell’s ideas. The chapter begins with displacement current, introduced to fix Ampere’s law for situations like a charging capacitor where conduction current exists in wires but not between plates. Maxwell showed that changing electric fields produce magnetic fields and changing magnetic fields produce electric fields, allowing self-sustaining electromagnetic waves to travel through space. These waves have mutually perpendicular electric and magnetic fields and can travel even in vacuum at speed c = 1/√(μ0ε0). The electromagnetic spectrum arranges radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays by wavelength and frequency. NEET mainly tests formulas, spectrum order, properties and applications.

Key Points6
  • 1Maxwell predicted electromagnetic waves theoretically before their experimental confirmation.
  • 2Displacement current ensures continuity of current in a charging capacitor.
  • 3EM waves do not require a material medium and can propagate through vacuum.
  • 4In an EM wave, E/B = c in vacuum.
  • 5Visible light is only a small part of the electromagnetic spectrum.
  • 6Different EM waves differ mainly in frequency and wavelength, not in nature.
Memory Tricks2

Spectrum Order

Remember wavelength decreasing order: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma.

EM Wave Orientation

E, B and direction of travel are mutually perpendicular like three coordinate axes.

Examples2

Real-Life Example

Your phone uses radio or microwave electromagnetic waves to communicate without wires.

NEET-Style Snapshot

If an EM wave has frequency 6 × 10¹⁴ Hz, its wavelength in vacuum is λ = c/f = 3 × 10⁸/(6 × 10¹⁴) = 5 × 10⁻⁷ m.

Reference Tables2
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Common Mistakes2

Saying EM Waves Need Medium

Electromagnetic waves can travel in vacuum because changing electric and magnetic fields sustain each other.

Reversing Frequency and Wavelength Order

As wavelength decreases, frequency increases because c = fλ.

Formula Cards5
Displacement Current

Current equivalent produced by a changing electric flux.

Variables

ID=

Displacement current

ε0=

Permittivity of free space

ΦE=

Electric flux

t=

Time

Ampere-Maxwell Law

Modified Ampere’s law including both conduction current and displacement current.

Variables

B=

Magnetic field

dl=

Small path element

IC=

Conduction current

ID=

Displacement current

μ0=

Permeability of free space

Speed of Electromagnetic Waves

Speed of electromagnetic waves in vacuum.

Variables

c=

Speed of light in vacuum

μ0=

Permeability of free space

ε0=

Permittivity of free space

Diagrams3
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2

Displacement Current

Overview

Displacement current was introduced by Maxwell to remove an inconsistency in Ampere’s circuital law. During charging of a capacitor, conduction current flows in the wires, but no actual charge crosses the gap between plates. Still, the magnetic field around the circuit is continuous, so Maxwell proposed that a changing electric field between the capacitor plates acts like a current. This is called displacement current, ID = ε0 dΦE/dt. It is not due to physical flow of charges across the dielectric or vacuum gap, but due to changing electric flux. Including it gives Ampere-Maxwell law: ∮B·dl = μ0(IC + ID). Displacement current is essential for continuity of current and for the existence of electromagnetic waves.

Key Points6
  • 1Maxwell introduced displacement current as a correction to Ampere’s law.
  • 2It is not a current of moving free charges through the capacitor gap.
  • 3A changing electric field produces magnetic field just as conduction current does.
  • 4Displacement current is present in vacuum if electric field changes with time.
  • 5It preserves continuity of current in circuits with capacitors.
  • 6It is one of the key ideas leading to prediction of electromagnetic waves.
Memory Tricks2

Why Displacement Current?

Capacitor gap has no charge crossing, but changing electric field continues the current effect.

Maxwell Correction

Ampere needed Maxwell’s missing current: conduction plus displacement.

Examples2

Numerical Example

If electric flux through a capacitor changes at 5 × 10¹¹ N m² C⁻¹ s⁻¹, then ID = ε0 dΦE/dt = 8.85 × 10⁻¹² × 5 × 10¹¹ = 4.425 A.

Concept Example

A steady charged capacitor has constant electric field, so displacement current is zero because dΦE/dt = 0.

Reference Tables2
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Common Mistakes2

Thinking Displacement Current Is Charge Flow Across Vacuum

Displacement current is not actual movement of free charges through vacuum; it is due to changing electric field.

Ignoring Displacement Current in Capacitor Gap

During charging, displacement current between plates equals conduction current in the wires.

Formula Cards4
Displacement Current

Current equivalent due to changing electric flux.

Variables

ID=

Displacement current

ε0=

Permittivity of free space

ΦE=

Electric flux

t=

Time

Displacement Current Density

Displacement current per unit area for a uniform changing electric field.

Variables

JD=

Displacement current density

E=

Electric field

t=

Time

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3

Electromagnetic Waves

Overview

Maxwell predicted that changing electric and magnetic fields can sustain each other and travel through space as electromagnetic waves. An electromagnetic wave consists of oscillating electric field and magnetic field that are perpendicular to each other and also perpendicular to the direction of propagation. Hence EM waves are transverse waves. They do not require any material medium and can travel through vacuum. In vacuum their speed is c = 1/√(μ0ε0), equal to approximately 3 × 10⁸ m/s. The electric and magnetic fields are in the same phase, and their amplitudes satisfy E0/B0 = c. All electromagnetic waves obey v = fλ, where f is frequency, λ is wavelength and v is wave speed.

Key Points6
  • 1The electric and magnetic fields of an EM wave are in the same phase.
  • 2EM waves carry energy and momentum.
  • 3No material medium is needed for propagation.
  • 4All EM waves travel at the same speed in vacuum but differ in frequency and wavelength.
  • 5In a medium, speed is less than c and depends on the medium.
  • 6The direction of propagation is given by E × B.
Memory Tricks2

E-B-Direction

Use E cross B to remember propagation direction.

v = fλ

Wave speed equals how many waves per second times length of each wave.

Examples2

Given Wave Relation Example

If f = 2 Hz and λ = 3 m, then v = fλ = 2 × 3 = 6 m/s.

NEET-Type Numerical

If E0 = 300 V/m in vacuum, then B0 = E0/c = 300/(3 × 10⁸) = 1 × 10⁻⁶ T.

Reference Tables2
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Common Mistakes2

Thinking E and B Are Out of Phase

In an EM wave, electric and magnetic fields are in the same phase.

Calling EM Waves Longitudinal

Electromagnetic waves are transverse because fields oscillate perpendicular to propagation.

Formula Cards4
Wave Relation

f is frequency; λ is wavelength; v is wave speed. Example: v = fλ = 2 × 3 = 6 m/s.

Variables

v=

Wave speed in m/s

f=

Frequency in Hz

λ=

Wavelength in m

Speed of Electromagnetic Waves in Vacuum

Speed of EM waves in free space.

Variables

c=

Speed of light in vacuum

μ0=

Permeability of free space

ε0=

Permittivity of free space

Diagrams3
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4

Electromagnetic Spectrum

Overview

The electromagnetic spectrum is the continuous arrangement of electromagnetic waves according to wavelength or frequency. All members are electromagnetic waves and travel with the same speed in vacuum, but they differ in wavelength, frequency, energy, production and applications. In decreasing wavelength order, the spectrum is radio waves, microwaves, infrared rays, visible light, ultraviolet rays, X-rays and gamma rays. Frequency and photon energy increase in the opposite direction. Radio waves are used in broadcasting and communication, microwaves in radar and ovens, infrared in thermal imaging, visible light in vision, ultraviolet in sterilization, X-rays in medical imaging and gamma rays in cancer treatment. NEET frequently asks the correct order and applications.

Key Points6
  • 1All electromagnetic waves have the same speed in vacuum.
  • 2Radio waves have the longest wavelength and lowest frequency among the listed types.
  • 3Gamma rays have the shortest wavelength and highest frequency.
  • 4Visible light occupies only a narrow band of the spectrum.
  • 5Infrared is emitted strongly by warm bodies.
  • 6X-rays are produced by sudden deceleration of high-speed electrons, while gamma rays originate from nuclear transitions.
Memory Tricks2

Spectrum Mnemonic

Raging Martians Invaded Venus Using X-ray Guns: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma.

Energy Trend

Gamma is greatest energy; Radio is relaxed and lowest energy.

Examples2

Order Example

Correct increasing frequency order is radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays.

Wavelength Example

If two EM waves are radio and X-rays, radio has much longer wavelength and much lower frequency.

Reference Tables2
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Common Mistakes2

Placing Visible Before Infrared

In increasing frequency order, infrared comes before visible and ultraviolet comes after visible.

Thinking X-rays and Gamma Rays Differ Only by Wavelength

They overlap in wavelength sometimes, but typically differ by origin: X-rays from electronic processes and gamma rays from nuclear processes.

Formula Cards3
Wave Relation for Spectrum

In vacuum, frequency and wavelength of electromagnetic waves are inversely related.

Variables

c=

Speed of light in vacuum

f=

Frequency

λ=

Wavelength

Photon Energy Relation

Energy of electromagnetic radiation increases with frequency.

Variables

E=

Photon energy

h=

Planck constant

f=

Frequency

Diagrams3
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5

Applications

Overview

Electromagnetic waves are used in daily life, medicine, communication, industry and research according to their wavelength, frequency and penetration ability. Radio waves are used in communication systems such as broadcasting, mobile communication and satellite links. Microwaves are used in radar because they reflect from aircraft and ships, and in microwave ovens because water molecules absorb microwave energy and heat food. Infrared radiation is used in remote controls, thermal imaging and night vision. Ultraviolet rays kill microorganisms and are used for sterilization. X-rays penetrate soft tissues but are absorbed more by bones, making them useful in medical imaging. Gamma rays have very high energy and are used in cancer treatment to destroy malignant cells.

Key Points6
  • 1Microwave ovens heat food mainly by energy absorption in water molecules.
  • 2Radar detects objects by sending microwaves and receiving reflected waves.
  • 3Infrared cameras detect heat emitted by bodies.
  • 4UV rays can damage living cells, so controlled use is necessary.
  • 5X-ray imaging requires shielding and limited exposure.
  • 6Gamma rays can kill cancer cells but must be precisely targeted.
Memory Tricks2

Application Mapping

Radio talks, Microwave cooks and detects, Infrared heats, UV sterilizes, X-ray images, Gamma treats cancer.

Safety Trend

Higher frequency generally means higher photon energy, so UV, X-rays and gamma rays need more caution.

Examples3

Communication Systems

Radio and microwave signals carry voice, video and data in broadcasting, mobile networks, Wi-Fi and satellite communication.

Medical Applications

X-ray imaging helps observe bones and internal structures, while gamma rays can be focused to destroy cancer cells.

Sterilization Example

UV lamps are used to sterilize water and surfaces because UV radiation damages microorganisms.

Reference Tables2
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Common Mistakes3

Mixing Microwave and Infrared Heating

Microwave ovens mainly heat water-containing food internally; infrared heating is surface heat radiation from hot bodies.

Assuming X-rays and Gamma Rays Are Safe Because Useful

Both are ionising radiations and must be used with controlled exposure and shielding.

Forgetting Radio Waves Are EM Waves

Radio waves are electromagnetic waves just like light; they simply have much longer wavelength.

Formula Cards3
Radar Distance Basic Relation

Distance of an object from radar when reflected signal returns after time t.

Variables

d=

Distance of object

c=

Speed of electromagnetic wave

t=

Round-trip time delay

Wave Relation in Applications

Used to connect frequency and wavelength for EM waves in vacuum or air approximately.

Variables

c=

Speed of light

f=

Frequency

λ=

Wavelength

Diagrams4
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Formula Sheet

10
Displacement Current

Current equivalent produced by a changing electric flux.

Variables

ID=

Displacement current

ε0=

Permittivity of free space

ΦE=

Electric flux

t=

Time

Ampere-Maxwell Law

Modified Ampere’s law including both conduction current and displacement current.

Variables

B=

Magnetic field

dl=

Small path element

IC=

Conduction current

ID=

Displacement current

μ0=

Permeability of free space

Speed of Electromagnetic Waves

Speed of electromagnetic waves in vacuum.

Variables

c=

Speed of light in vacuum

μ0=

Permeability of free space

ε0=

Permittivity of free space

Wave Relation

Relation between wave speed, frequency and wavelength.

Variables

v=

Wave speed

f=

Frequency

λ=

Wavelength

Field Ratio in Vacuum

Ratio of electric field amplitude to magnetic field amplitude in an electromagnetic wave.

Variables

E0=

Amplitude of electric field

B0=

Amplitude of magnetic field

c=

Speed of electromagnetic wave in vacuum

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NEET PYQs — Electromagnetic Waves

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NEET 2026Set 11EasyQ1

Match List-I with List-II: Choose the correct answer from the options given below:

NEET 2025Set E45MediumQ2

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is :

NEET 2025Set 45MediumQ3

The electric field in a plane electromagnetic wave is given by: $$E_z = 60\cos\left(5x + 1.5 \times 10^9 t\right)\ \text{V/m}$$ Then the expression for the corresponding magnetic field is (here subscripts denote the direction of the field):

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