Electromagnetic Waves shows how Maxwell completed the laws of electricity and magnetism by adding the displacement current, leading to the prediction that changing electric and magnetic fields sustain each other and travel as a wave at the speed of light even through vacuum. The chapter covers the transverse nature of EM waves, the speed relation c equals 1 over the square root of mu-naught times epsilon-naught, their energy, momentum and radiation pressure, and the full electromagnetic spectrum with the sources and uses of each band. It is a short, high-yield NEET chapter where most questions are direct recall of the spectrum order, key formulas and characteristic uses.
Key Concepts
1. Displacement Current and Maxwell’s Equations
Maxwell showed that a changing electric field produces a magnetic field, just as a changing magnetic field produces an electric field (Faraday’s law). He introduced the concept of displacement current:
Id = ε₀(dΦE/dt)
This completed Ampere’s law: ∮B·dl = μ₀(Ic + Id), making the equations symmetric.
2. Properties of EM Waves
- Produced by accelerating charges
- Do not need a medium - travel through vacuum at speed c = 3 × 10⁸ m/s
- E and B fields are perpendicular to each other and to the direction of propagation (transverse waves)
- c = 1/√(μ₀ε₀) = E₀/B₀
- Carry energy and momentum
- Follow c = fλ
3. Electromagnetic Spectrum
| Wave Type | Frequency Range | Wavelength Range | Source | Uses |
|---|---|---|---|---|
| Radio waves | < 10⁹ Hz | > 0.3 m | Oscillating circuits | Radio/TV broadcasting, communication |
| Microwaves | 10⁹ – 10¹¹ Hz | 0.3 m – 1 mm | Klystron, magnetron | Microwave oven, radar, satellite communication |
| Infrared | 10¹¹ – 4×10¹⁴ Hz | 1 mm – 700 nm | Hot bodies | Night vision, remote controls, greenhouse effect |
| Visible light | 4×10¹⁴ – 8×10¹⁴ Hz | 700 – 400 nm | Sun, lamps | Vision, photosynthesis |
| Ultraviolet | 8×10¹⁴ – 10¹⁶ Hz | 400 – 1 nm | Sun, mercury lamp | Sterilisation, LASIK, vitamin D production |
| X-rays | 10¹⁶ – 10¹⁹ Hz | 1 nm – 10⁻³ nm | X-ray tube (bombarding metal with electrons) | Medical imaging, security screening |
| Gamma rays | > 10¹⁹ Hz | < 10⁻³ nm | Radioactive decay, nuclear reactions | Cancer treatment, sterilisation |
Order of increasing frequency: Radio < Microwave < IR < Visible < UV < X-ray < Gamma
Order of increasing wavelength: Gamma < X-ray < UV < Visible < IR < Microwave < Radio
Solved Examples
Example 1
An EM wave has frequency 5 × 10¹⁴ Hz. Find its wavelength and identify the type.
Answer: λ = c/f = (3 × 10⁸)/(5 × 10¹⁴) = 6 × 10⁻⁷ m = 600 nm. This is visible light (orange-red).
Example 2
The electric field in an EM wave has amplitude 100 V/m. Find the amplitude of the magnetic field.
Answer: B₀ = E₀/c = 100/(3 × 10⁸) = 3.33 × 10⁻⁷ T
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Important Questions for Board Exams
1-Mark
- What is displacement current?
- Which EM wave is used in RADAR?
3-Mark
- List the electromagnetic spectrum in order of increasing frequency. Give one use of each type.
- State the properties of electromagnetic waves.
5-Mark
- Describe the electromagnetic spectrum in detail. Give the source, frequency range, and applications for each type of EM wave.
Quick Revision Points
- EM waves: E ⊥ B ⊥ direction of propagation; travel at c = 3 × 10⁸ m/s in vacuum
- c = 1/√(μ₀ε₀) = E₀/B₀ = fλ
- Displacement current Id = ε₀(dΦE/dt) - completes Ampere’s law
- Spectrum (↑ frequency): Radio → Microwave → IR → Visible → UV → X-ray → Gamma
- Radio: broadcasting; Microwave: radar, ovens; IR: night vision; UV: sterilisation; X-ray: imaging; Gamma: cancer treatment
Previous: Ch 7 - Alternating Current
Next: Ch 9 - Ray Optics
Class 12 Physics · Chapter 8 – swipe through all 10 cards to understand the whole chapter.
The Big Picture
A changing electric field makes a magnetic field and a changing magnetic field makes an electric field, so they sustain each other and travel as a wave even through vacuum.
No medium needed; this is why sunlight crosses empty space.
- Maxwell unified electricity, magnetism and light
- EM waves carry energy and momentum but no charge
- Produced only by accelerating (e.g. oscillating) charges
Displacement Current
Ampere’s law failed for a charging capacitor, so Maxwell added a current due to a changing electric field between the plates.
No charge crosses the gap; it is a time-varying electric flux Φ_E.
- In a capacitor, I_d between plates = conduction current I_c in wire
- Exists wherever E changes with time, not only in capacitors
- Makes B continuous across the plate gap
Ampere–Maxwell Law
The corrected circuital law adds the displacement-current term to the real conduction current.
The added term is what predicts electromagnetic waves.
- Symmetric with Faraday: changing E makes B, changing B makes E
- Same B whether the loop sits in the wire or the gap
- Whole set of Maxwell’s equations now self-consistent
Nature of EM Waves
EM waves are transverse: E and B are perpendicular to each other and to the direction of travel, oscillating in phase.
E and B peak together and vanish together (in phase).
- Wave travels along E × B (right-handed set)
- Not deflected by electric or magnetic fields (no charge)
- Energy shared equally between E and B fields
Speed of EM Waves
In vacuum the speed depends only on two properties of free space and equals the speed of light.
In a medium v = c / n < c; never write c = √(μ0ε0).
- All EM waves travel at c in vacuum
- In glass the wave slows to c/n: λ shrinks, f stays fixed
- Light is just one kind of EM wave
E0 and B0 Locked Together
At every instant the electric field strength is c times the magnetic field strength.
This is why E (V m⁻1) is numerically far larger than B (T).
- The factor between them is c ≈ 3 × 108
- E and B amplitudes rise and fall together
- Use it to convert between the two amplitudes
Energy Density
Both fields store energy, and on average each carries exactly half the total.
For averages use rms values: E_rms = E0 / √2.
- Energy split 50-50 between E and B
- Intensity I = ½ ε0 E02 c (energy per area per second)
- The ½ in average formulas comes from using rms fields
Radiation Pressure
EM waves carry momentum, so absorbing or reflecting light delivers a tiny push.
Reflection doubles the momentum transfer and pressure vs absorption.
- Force on absorber F = P/c (P = power)
- Perfect reflector feels twice the force, F = 2P/c
- This is how solar sails work
The EM Spectrum
All EM waves are the same phenomenon; they differ only in frequency and wavelength.
VIBGYOR: Violet highest f, Red lowest f within visible light.
- c = fλ, so higher f ⇒ shorter λ ⇒ more energetic photons (E = hf)
- Ozone absorbs UV; IR is the ‘heat wave’
- X-rays: fast electrons on metal; Gamma: nuclei / radioactive decay
Spectrum at a Glance
Each band has a characteristic source and everyday use worth memorising for NEET.
Visible light spans roughly 400–700 nm.
- Radio: antennas/circuits → TV, mobile; Microwave: magnetron → radar, ovens
- IR: hot bodies → remotes, thermography; UV: Sun → sterilisation, sunburn
- X-ray: medical imaging; Gamma: cancer therapy
📝 Practice Electromagnetic Waves — 10 NEET PYQs
Real previous-year questions · with answers & solutions
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Chapter Navigation
Previous: Alternating Current Class 12 Notes
Next: Ray Optics and Optical Instruments Class 12 Notes
Related Chapters in Class 12 Physics
- Alternating Current Class 12 Notes
- Ray Optics and Optical Instruments Class 12 Notes
- Wave Optics Class 12 Notes
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Frequently Asked Questions
Displacement current is the current associated with a changing electric field, given by I_d equals epsilon-naught times the rate of change of electric flux. Maxwell added it because Ampere’s law gave no magnetic field between the plates of a charging capacitor, where no conduction current flows, even though a magnetic field clearly exists there.
In vacuum every EM wave travels at the speed of light, c equals 1 over the square root of mu-naught times epsilon-naught, which is about 3 times 10 to the power 8 metres per second. In a medium the speed drops to v equals c divided by the refractive index n, so it is always less than c.
At every instant the electric field is c times the magnetic field, so E-naught divided by B-naught equals c and E equals cB. The E and B fields are perpendicular to each other and to the direction of travel, and they oscillate in phase, peaking and vanishing together.
In order of increasing frequency and decreasing wavelength it is radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Useful tags to remember are infrared as heat waves, ozone absorbing UV, X-rays from fast electrons hitting metal and gamma rays from nuclei.
An EM wave carries momentum p equals U divided by c for energy U, so a fully absorbing surface receives momentum U over c, but a perfectly reflecting surface receives twice that, 2U over c, because the wave reverses direction. This is why a perfect reflector feels double the force and pressure compared with a perfect absorber.