Chapter 8: Electromagnetic Waves Long Questions | physics Class 12 CBSE

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Chapter 8: Electromagnetic Waves Long Questions | physics Class 12 CBSE | ByteNotes.in

Long Answer

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Question 1

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Analyse Maxwell's modification of Ampere's circuital law. How does the concept of displacement current resolve the inconsistency? Derive the expression for displacement current.

Maxwell applied Ampere's law to a charging capacitor using two different surfaces sharing the same boundary: a flat surface intercepting the wire (gives B(2πr) = µ₀i) and a pot-shaped surface passing between the capacitor plates (gives B(2πr) = 0, since no conduction current passes through). This contradiction showed that Ampere's law was incomplete.
Maxwell identified that between the capacitor plates, the electric flux Φ_E = Q/ε₀ is changing with time as the capacitor charges. The rate of change is dΦ_E/dt = (1/ε₀)(dQ/dt) = i/ε₀, implying ε₀(dΦ_E/dt) = i.
Maxwell introduced the displacement current iₐ = ε₀(dΦ_E/dt) as the missing term. Adding this to Ampere's law gives the Ampere-Maxwell law: ∮B·dl = µ₀(iₓ + iₐ) = µ₀iₓ + µ₀ε₀(dΦ_E/dt).
With this modification, the total current (iₓ + iₐ) is the same value i for both surfaces — equal to the conduction current outside the plates and to the displacement current between the plates — removing the contradiction.
The displacement current has the same physical effect as conduction current in generating magnetic fields. This result also makes the laws of electricity and magnetism more symmetrical: just as changing B produces E (Faraday's law), changing E produces B (Ampere-Maxwell law).

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Question 2

Long Form

Compare the properties of electromagnetic waves in vacuum versus in a material medium. How does the medium affect the speed and what are the implications for optics?

In vacuum, EM waves travel at speed c = 1/√(µ₀ε₀) ≈ 3 × 10⁸ m/s. This speed is independent of wavelength, meaning all frequencies of EM radiation travel at the same speed in free space.
In a material medium with permittivity ε and permeability µ, the speed reduces to v = 1/√(µε). Since ε > ε₀ and µ ≥ µ₀ for most materials, v < c.
The ratio c/v gives the refractive index of the medium, connecting Maxwell's electromagnetic theory directly to the phenomenon of refraction studied in optics.
In vacuum, EM waves need no material medium and are self-sustaining oscillations of E and B fields. In a medium, the fields interact with the atoms and molecules, described by the medium's permittivity and permeability.
The constancy of c in vacuum is so precisely established that it now defines the SI standard of length: 1 metre is defined as the distance light travels in 1/299,792,458 of a second.

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Question 3

Long Form

Describe the mathematical representation of a plane electromagnetic wave propagating along the z-direction. Derive the relation between the angular frequency, wave number, and speed of the wave.

A plane EM wave propagating along the z-axis has its electric field along the x-axis and magnetic field along the y-axis: Eₓ = E₀ sin(kz − ωt) and B_y = B₀ sin(kz − ωt), where both fields oscillate in phase.
The wave number k = 2π/λ relates to the wavelength, and ω = 2πν relates to the frequency ν. The direction of k is the direction of propagation.
From Maxwell's equations, substituting the sinusoidal forms of E and B, one finds ω = ck, where c = 1/√(µ₀ε₀). This is the standard dispersion relation for EM waves.
The relation ω = ck can be written as νλ = c, the familiar wave equation linking frequency, wavelength, and wave speed. The speed of propagation is ω/k = c.
Additionally, Maxwell's equations give B₀ = E₀/c, showing that the magnetic field amplitude is always much smaller than the electric field amplitude (in SI units), since c is large.

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Question 4

Long Form

Explain how Maxwell's equations unify electricity, magnetism, and optics. What was the historical significance of this unification?

Maxwell's four equations (Gauss's laws, Faraday's law, Ampere-Maxwell law) together describe all electromagnetic phenomena, showing electricity and magnetism as two aspects of a single unified force.
From these equations, Maxwell predicted self-propagating electromagnetic waves with speed c = 1/√(µ₀ε₀). When calculated, this value matched the experimentally known speed of light almost exactly, leading to the conclusion that light is an electromagnetic wave.
This unified the domain of optics (previously a separate science) with electromagnetism, reducing three distinct fields — electricity, magnetism, and light — to one consistent theoretical framework.
Hertz's 1887 experiment confirmed the existence of EM waves in the radio frequency range, verifying Maxwell's theoretical prediction and sparking the development of wireless communication technology.
The unification is historically one of the greatest achievements in physics, comparable to Newton's unification of celestial and terrestrial mechanics; it also laid the groundwork for Einstein's theory of special relativity.

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Question 5

Long Form

Discuss the role of accelerated charges in the production of electromagnetic waves. Why can neither stationary charges nor uniform motion charges produce EM waves?

Stationary charges produce only static (time-independent) electric fields — there is no change in field with time, so no magnetic field is generated and no EM wave is produced.
Charges in uniform motion (steady currents) produce magnetic fields that do not vary with time; without a time-varying magnetic field, no electromagnetic induction occurs and no EM wave results.
Accelerated charges, however, produce time-varying electric fields, which generate time-varying magnetic fields, which in turn regenerate electric fields — creating self-sustaining EM waves that propagate outward.
A charge oscillating with frequency ν is an accelerating charge; it produces oscillating E and B fields of the same frequency ν. An electric dipole is a basic source of EM radiation.
The energy carried by the EM wave comes at the expense of the kinetic energy of the accelerated charge — the source loses energy as it radiates.

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Question 6

Long Form

Describe the electromagnetic spectrum in detail. How are the different regions classified, and what is common among all types of EM waves?

The EM spectrum ranges from gamma rays (λ ~ 10⁻¹² m, highest frequency) to long radio waves (λ ~ 10⁶ m, lowest frequency). The classification is based on how waves are produced or detected, with no sharp boundary between adjacent regions.
In order of increasing wavelength: gamma rays (from nuclear decay, λ < 10⁻¹⁰ m), X-rays (from heavy atom transitions, 10⁻¹³ to 10⁻⁸ m), UV rays (very hot bodies, ~ 1 nm to 400 nm), visible light (400–700 nm), infrared (700 nm to 1 mm), microwaves (1 mm to 0.1 m), radio waves (> 0.1 m).
All EM waves travel through vacuum at the same speed c = 3 × 10⁸ m/s and consist of mutually perpendicular oscillating E and B fields, both perpendicular to the direction of propagation.
They differ in frequency (wavelength), which determines how they interact with matter — gamma rays and X-rays are highly penetrating and ionising; radio waves pass through most materials with little absorption.
All EM waves carry energy from one place to another via their oscillating fields; this energy transport is what makes them technologically vital in communication, medicine, astronomy, and industry.

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Question 7

Long Form

Analyse the greenhouse effect in terms of electromagnetic waves. How do infrared waves and visible light play different roles in this phenomenon?

The sun emits radiation primarily in the visible range (~400–700 nm), which passes relatively easily through the earth's atmosphere and is absorbed by the earth's surface.
The earth's surface, now warmed, re-radiates energy as infrared (longer wavelength) radiation. Infrared is radiated because the earth is much cooler than the sun and radiates at lower frequencies.
Greenhouse gases such as carbon dioxide (CO₂) and water vapour readily absorb infrared radiation because their molecular resonant frequencies lie in the infrared range, trapping heat near the earth's surface.
This trapping of infrared radiation is the greenhouse effect — it maintains the earth's average temperature above what it would otherwise be, making life possible.
Infrared waves are sometimes called heat waves because they increase the thermal (kinetic) energy of molecules upon absorption. The differential transparency of the atmosphere to visible and infrared is the key to understanding the greenhouse effect.

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Question 8

Long Form

Compare and contrast the production, detection, and uses of microwaves and radio waves based on the chapter.

Radio waves (frequency 500 kHz to 1000 MHz) are produced by rapid acceleration and deceleration of electrons in conducting aerials, while microwaves (GHz range) are produced by special vacuum tubes such as klystrons, magnetrons, and Gunn diodes.
Radio waves are detected by receiver aerials, while microwaves are detected by point contact diodes — reflecting the difference in their wavelengths and the size of structures needed to interact with them.
Radio waves are used in AM/FM radio (530 kHz–108 MHz), television broadcasting (54–890 MHz), and cellular communication (UHF band); microwaves are used in radar systems for navigation and speed measurement.
A key microwave application is the domestic microwave oven, where the frequency is tuned to the resonant frequency of water molecules, enabling efficient heating of food. Radio waves have no analogous thermal application.
Both radio waves and microwaves are classified under long-to-medium wavelength EM radiation, and both travel at c in vacuum. The distinction between them is quantitative (frequency/wavelength) rather than qualitative.

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Question 9

Long Form

Critically examine the symmetry between Faraday's law and the Ampere-Maxwell law. How does this symmetry lead to the prediction of electromagnetic waves?

Faraday's law states: ∮E·dl = −dΦ_B/dt — a changing magnetic field produces an electric field. This is the foundation of electromagnetic induction.
The Ampere-Maxwell law states: ∮B·dl = µ₀iₓ + µ₀ε₀(dΦ_E/dt) — a changing electric field (displacement current) produces a magnetic field. This is the symmetrical counterpart introduced by Maxwell.
Together, the two laws create a feedback loop: a time-varying E produces B (Ampere-Maxwell), and the resulting time-varying B produces E (Faraday). This mutual regeneration is self-sustaining.
If no medium or charges are present, both conduction current and free charges are absent. Yet the E and B fields regenerate each other, propagating as a transverse wave — this is an electromagnetic wave.
The asymmetry is that there are no magnetic monopoles (sources of B analogous to charges as sources of E), but this does not prevent the mutual regeneration. The speed of this propagating disturbance is exactly c = 1/√(µ₀ε₀), confirming it is an EM wave.

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Question 10

Long Form

Explain the applications of ultraviolet rays in medicine and technology, and discuss the hazards associated with UV exposure.

UV radiation covers wavelengths from about 400 nm down to 0.6 nm. Due to its shorter wavelengths, UV can be focused into very narrow beams, enabling high-precision applications such as LASIK eye surgery.
UV lamps are used to kill germs in water purifiers by destroying the DNA and cellular structures of microorganisms, making UV an effective sterilisation tool.
Welders are exposed to large amounts of UV from welding arcs; they must wear special glass goggles or face masks since ordinary glass absorbs UV and protects the eyes.
In large quantities, UV radiation has harmful effects: it induces excess melanin production (causing skin tanning and potentially skin cancer) and can damage living tissues and organisms.
The ozone layer at 40–50 km altitude naturally absorbs most of the sun's UV radiation, protecting life on earth. Depletion of this ozone layer by CFCs (such as freon) is an international environmental concern.

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Chapter 8: Electromagnetic Waves | Long Questions

Analyse Maxwell's modification of Ampere's circuital law. How does the concept of displacement current resolve the inconsistency? Derive the expression for displacement current.

Compare the properties of electromagnetic waves in vacuum versus in a material medium. How does the medium affect the speed and what are the implications for optics?

Describe the mathematical representation of a plane electromagnetic wave propagating along the z-direction. Derive the relation between the angular frequency, wave number, and speed of the wave.

Explain how Maxwell's equations unify electricity, magnetism, and optics. What was the historical significance of this unification?

Discuss the role of accelerated charges in the production of electromagnetic waves. Why can neither stationary charges nor uniform motion charges produce EM waves?

Describe the electromagnetic spectrum in detail. How are the different regions classified, and what is common among all types of EM waves?

Analyse the greenhouse effect in terms of electromagnetic waves. How do infrared waves and visible light play different roles in this phenomenon?

Compare and contrast the production, detection, and uses of microwaves and radio waves based on the chapter.

Critically examine the symmetry between Faraday's law and the Ampere-Maxwell law. How does this symmetry lead to the prediction of electromagnetic waves?

Explain the applications of ultraviolet rays in medicine and technology, and discuss the hazards associated with UV exposure.

Unlock all Long Questions