CHAPTER 8: ELECTROMAGNETIC WAVES
SAMPLE QUESTION PAPER (ASSIGNMENT-1)
- There are 33 questions in all. All questions are compulsory.
- Section A: 16 questions (12 MCQs and 4 Assertion-Reasoning) of 1 mark each.
- Section B: 5 short answer questions of 2 marks each.
- Section C: 7 short answer questions of 3 marks each.
- Section D: 2 case study-based questions of 4 marks each.
- Section E: 3 long answer questions of 5 marks each.
SECTION A (16 Marks)
Q.1. In an electromagnetic wave, according to James Clerk Maxwell, a time-varying electric field gives rise to:
Explanation: A changing electric field gives rise to displacement current $\displaystyle {I_d = \varepsilon_0 {\frac{{d\Phi_E}}{{dt}}}}$, which acts as a source of magnetic field.
Q.2. The electric and magnetic fields ($\displaystyle {\vec{E}}$ and $\displaystyle {\vec{B}}$) of a plane electromagnetic wave are:
Explanation: In an EM wave, $\displaystyle {\vec{E}}$ and $\displaystyle {\vec{B}}$ reach their maxima and minima at the same time and place (in phase) and oscillate perpendicular to each other and to the direction of propagation.
Q.3. For a material medium with permittivity $\displaystyle {\varepsilon}$ and magnetic permeability $\displaystyle {\mu}$, the velocity of light $\displaystyle {v}$ is given by:
Explanation: Speed of EM wave in a medium is $\displaystyle {v = {\frac{{1}}{{\sqrt{\mu \varepsilon}}}} = {\frac{{c}}{{\sqrt{\mu_r \varepsilon_r}}}}}$.
Q.4. The electric and magnetic fields of a plane EM wave propagating along the $\displaystyle {+Y}$ axis are represented by:
Explanation: Direction of wave propagation is given by Poynting vector $\displaystyle {\vec{E} \times \vec{B}}$. Here $\displaystyle {\hat{k} \times \hat{i} = \hat{j}}$, which corresponds to $\displaystyle {+Y}$ axis.
Q.5. A plane EM wave of frequency $\displaystyle {20\text{ MHz}}$ travels along $\displaystyle {+X}$ axis. At a point, electric field vector is $\displaystyle {6\text{ V/m}}$. What is the magnitude of the magnetic field at that point?
Explanation: Ratio of amplitudes $\displaystyle {E_0 / B_0 = c \implies B_0 = {\frac{{E_0}}{{c}}} = {\frac{{6}}{{3 \times 10^8}}} = 2 \times 10^{-8}\text{ T}}$.
Q.6. The average magnetic energy density ($\displaystyle {u_B}$) of an EM wave with magnetic field amplitude $\displaystyle {B_0}$ is:
Explanation: Average magnetic energy density is $\displaystyle {u_B = {\frac{{1}}{{2}}} \left({\frac{{B_{\text{rms}}^2}}{{\mu_0}}}\right) = {\frac{{B_0^2}}{{4\mu_0}}}}$, which equals average electric energy density $\displaystyle {u_E = {\frac{{1}}{{4}}} \varepsilon_0 E_0^2}$.
Q.7. The magnetic field of a plane EM wave is $\displaystyle {B_y = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t)\text{ T}}$. This radiation belongs to:
Explanation: Angular frequency $\displaystyle {\omega = 1.5 \times 10^{11}\text{ rad/s} \implies f = {\frac{{\omega}}{{2\pi}}} \approx 2.39 \times 10^{10}\text{ Hz} = 23.9\text{ GHz}}$, which falls in the microwave band ($\displaystyle {10^9 - 10^{11}\text{ Hz}}$).
Q.8. Which of the following electromagnetic radiations has the maximum wavelength?
Explanation: Radio waves have the lowest frequency and longest wavelength ($\displaystyle {\lambda > 0.1\text{ m}}$) in the EM spectrum.
Q.9. The wavelength of a radio wave having a frequency of $\displaystyle {1\text{ MHz}}$ ($\displaystyle {10^6\text{ Hz}}$) in vacuum is:
Explanation: $\displaystyle {\lambda = {\frac{{c}}{{f}}} = {\frac{{3 \times 10^8}}{{10^6}}} = 300\text{ m}}$.
Q.10. In the electromagnetic spectrum, the visible light spectrum region lies between:
Explanation: Visible light wavelength range ($\displaystyle {400\text{ nm} - 700\text{ nm}}$) lies directly between Infrared ($\displaystyle {> 700\text{ nm}}$) and Ultraviolet ($\displaystyle {< 400\text{ nm}}$).
Q.11. The specific region of the EM spectrum used in microwave ovens for cooking food is:
Explanation: Microwaves match the resonant rotational frequency of water molecules in food, transferring thermal energy efficiently via friction.
Q.12. Which component of solar radiation is primarily responsible for the greenhouse effect on Earth?
Explanation: Earth re-radiates absorbed solar energy as long-wavelength Infrared radiation, which is trapped by atmospheric gases ($\displaystyle {\text{CO}_2, \text{H}_2\text{O}}$ vapor).
Directions for Q.13 to Q.16:
(a) Both Assertion and Reason are true and Reason is correct explanation.
(b) Both Assertion and Reason are true but Reason is NOT correct explanation.
(c) Assertion is true but Reason is false.
(d) Both Assertion and Reason are false.
Q.13. Assertion (A): In an electromagnetic wave, electric and magnetic field variations are perpendicular to each other and to the direction of propagation.
Reason (R): Electromagnetic waves are fundamentally transverse in nature.
Q.14. Assertion (A): The frequency of an electromagnetic wave equals the frequency of oscillation of the charge producing it.
Reason (R): The energy carried by the propagating wave comes at the expense of the energy of the oscillating source.
Q.15. Assertion (A): When sunlight falls on our hand, we feel the warmth due to energy absorption.
Reason (R): Electromagnetic waves transfer momentum, but because speed of light $\displaystyle {c}$ is very large, momentum transferred is extremely small and pressure is unfelt.
Explanation: Warmth is felt due to energy absorption ($\displaystyle {E}$), while radiation pressure ($\displaystyle {P = I/c}$) is undetectable because $\displaystyle {c = 3 \times 10^8\text{ m/s}}$ makes momentum $\displaystyle {p = E/c}$ tiny.
Q.16. Assertion (A): Infrared waves are frequently called heat waves.
Reason (R): Water molecules present in most materials readily absorb infrared waves, increasing their thermal motion and temperature.
SECTION B (10 Marks)
Q.17. Gamma rays and radio waves travel with the same velocity in free space. Distinguish between them in terms of (i) origin, (ii) main application.
(i) Origin: Gamma rays originate from nuclear transitions and radioactive decay of atomic nuclei; Radio waves are produced by accelerated motion of charges in conducting wires/antennas.
(ii) Application: Gamma rays are used in cancer radiotherapy and sterilization; Radio waves are used in radio, TV, and cellular telecommunications.
Q.18. How was Ampere's circuital law modified by James Clerk Maxwell to include displacement current? Explain.
Generalized Ampere-Maxwell Law: $\displaystyle {\oint \vec{B} \cdot d\vec{l} = \mu_0 (I_c + I_d) = \mu_0 \left(I_c + \varepsilon_0 {\frac{{d\Phi_E}}{{dt}}}\right)}$.
Q.19. How are electromagnetic waves produced by an oscillating charge? What is the ultimate source of energy of EM waves?
Energy Source: The kinetic/electrical energy supplied by the external source that causes the charge to oscillate.
Q.20. Arrange the following EM radiations in ascending order of frequency: (i) Microwaves, (ii) Radio waves, (iii) X-rays, (iv) Gamma rays. State two uses of any one.
Ascending order of frequency: Radio waves < Microwaves < X-rays < Gamma ($\displaystyle {\gamma}$) rays.
Uses of X-rays: (1) Medical imaging to detect bone fractures, (2) Studying crystal structures via X-ray diffraction.
Q.21. How are X-rays produced? Write two important applications of X-rays.
Production: X-rays are produced when high-speed energetic electrons are suddenly decelerated upon striking a heavy metal target (like tungsten) in a Coolidge tube.
Applications: (1) Diagnostic radiography in medicine, (2) Security scanning at airports/customs.
SECTION C (21 Marks)
Q.22. (i) Depict a plane EM wave propagating along the $\displaystyle {+X}$ axis. Write expressions for its oscillating electric and magnetic fields.
(ii) State three main characteristics of EM waves.
(i) $\displaystyle {E_y = E_0 \sin(k x - \omega t)}$, $\displaystyle {B_z = B_0 \sin(k x - \omega t)}$, where $\displaystyle {E_0 / B_0 = c}$.
(ii) Characteristics:
1. Transverse nature ($\displaystyle {\vec{E} \perp \vec{B} \perp}$ propagation direction).
2. Travel in vacuum at universal speed $\displaystyle {c = 1/\sqrt{\mu_0 \varepsilon_0} \approx 3 \times 10^8\text{ m/s}}$.
3. Carry both energy density $\displaystyle {u = \frac{1}{2}\varepsilon_0 E_0^2}$ and momentum $\displaystyle {p = E/c}$.
Q.23. EM waves of wavelengths $\displaystyle {\lambda_1, \lambda_2, \lambda_3}$ are used in radar systems, water purifiers, and TV remotes respectively.
(i) Identify the electromagnetic waves.
(ii) Mention one source for each wave.
(i) $\displaystyle {\lambda_1}$ $\rightarrow$ Microwaves, $\displaystyle {\lambda_2}$ $\rightarrow$ Ultraviolet (UV) rays, $\displaystyle {\lambda_3}$ $\rightarrow$ Infrared (IR) rays.
(ii) Sources:
- Microwaves: Special vacuum tubes (Klystron / Magnetron).
- Ultraviolet rays: Mercury vapor lamps or electric arcs.
- Infrared rays: Hot bodies and vibrating molecules.
Q.24. Name the EM waves produced by: (i) Radioactive decay of nuclei, (ii) Welding arcs, (iii) Hot bodies. Write one use of each.
(i) Gamma ($\displaystyle {\gamma}$) rays: Used in targeted cancer radiotherapy.
(ii) Ultraviolet (UV) rays: Used for sterilizing surgical instruments.
(iii) Infrared (IR) rays: Used in night-vision equipment and thermal imaging.
Q.25. Name the EM waves with frequency ranges produced in: (i) Radioactive decay, (ii) Electric welding sparks, (iii) TV remote control.
(i) Gamma rays: Frequency range $\displaystyle {> 10^{18}\text{ Hz}}$ ($\displaystyle {10^{18} - 10^{22}\text{ Hz}}$).
(ii) Ultraviolet rays: Frequency range $\displaystyle {10^{15} - 10^{17}\text{ Hz}}$.
(iii) Infrared rays: Frequency range $\displaystyle {10^{12} - 10^{14}\text{ Hz}}$.
Q.26. (i) Why do welders wear special glass goggles while working?
(ii) Why are infrared waves called heat waves? State one application.
(iii) Name waves produced in nuclear radioactive decay.
(i) Electric welding arcs emit high-intensity Ultraviolet (UV) radiation, which can cause severe eye damage/cataracts; special goggles block UV rays.
(ii) IR waves are readily absorbed by water molecules in matter, increasing thermal kinetic motion and heating the surroundings. Application: Physiotherapy heat lamps.
(iii) Gamma ($\displaystyle {\gamma}$) rays ($\displaystyle {f \sim 10^{20}\text{ Hz}}$).
Q.27. (i) Name EM waves suitable for RADAR systems in aircraft navigation and state their frequency range.
(ii) If Earth had no atmosphere, would average surface temperature be higher or lower? Explain.
(iii) Justify why incident EM waves exert pressure on a surface.
(i) Microwaves ($\displaystyle {10^9\text{ Hz} - 10^{11}\text{ Hz}}$).
(ii) Lower, because the natural greenhouse effect would be absent, allowing heat to escape freely into space at night.
(iii) EM waves transport momentum $\displaystyle {p = E/c}$. When incident on a surface, momentum transfer creates a net force per unit area, exerting radiation pressure.
Q.28. (i) Name EM waves used for cancer treatment and state their frequency range.
(ii) Why is the thin ozone layer in the stratosphere crucial for human survival?
(iii) Why is momentum transferred by incident EM waves so small?
(i) Gamma rays ($\displaystyle {10^{18} - 10^{22}\text{ Hz}}$).
(ii) The ozone layer absorbs harmful solar Ultraviolet (UV-B/UV-C) radiation, preventing skin cancer, eye cataracts, and cellular damage.
(iii) Momentum $\displaystyle {p = E/c}$ is extremely small because the speed of light $\displaystyle {c = 3 \times 10^8\text{ m/s}}$ in the denominator is extremely large.
SECTION D: CASE STUDY QUESTIONS (8 Marks)
Q.29. Case Study 1: Electromagnetic Spectrum & Applications.
The EM spectrum spans frequencies from $\displaystyle {10^3\text{ Hz}}$ (radio waves) to $\displaystyle {10^{22}\text{ Hz}}$ (gamma rays). All EM waves travel at speed $\displaystyle {c = 3 \times 10^8\text{ m/s}}$ in vacuum, obeying $\displaystyle {c = \nu \lambda}$.
(i) Which EM wave is used in medical imaging of bones?
(a) Gamma rays (b) X-rays (c) Infrared (d) Microwaves
(ii) Arrange in ascending order of frequency: Infrared, Radio waves, X-rays, Gamma rays.
(iii) Angle between electric field $\displaystyle {\vec{E}}$ and magnetic field $\displaystyle {\vec{B}}$ in an EM wave is:
(a) $\displaystyle {0^\circ}$ (b) $\displaystyle {45^\circ}$ (c) $\displaystyle {90^\circ}$ (d) $\displaystyle {180^\circ}$
(iv) Frequency of an EM wave of wavelength $\displaystyle {500\text{ km}}$ in vacuum is:
(a) $\displaystyle {600\text{ Hz}}$ (b) $\displaystyle {500\text{ Hz}}$ (c) $\displaystyle {167\text{ Hz}}$ (d) $\displaystyle {15\text{ Hz}}$
(i) (b) X-rays.
(ii) Radio waves < Infrared < X-rays < Gamma rays.
(iii) (c) $\displaystyle {90^\circ}$ ($\displaystyle {\vec{E} \perp \vec{B}}$).
(iv) (a) $\displaystyle {600\text{ Hz}}$ ($\displaystyle {\nu = c/\lambda = 3 \times 10^8 / (5 \times 10^5) = 600\text{ Hz}}$).
Q.30. Case Study 2: Maxwell's Displacement Current & Energy Density.
Maxwell proposed that changing electric fields induce magnetic fields, adding displacement current $\displaystyle {I_d = \varepsilon_0 d\Phi_E / dt}$ to Ampere's law.
(i) Total energy density of EM waves in vacuum is given by:
(a) $\displaystyle {\frac{1}{2}\varepsilon_0 E^2 + \frac{B^2}{2\mu_0}}$ (b) $\displaystyle {\frac{1}{2}\varepsilon_0 E^2 + \frac{1}{2}\mu_0 B^2}$ (c) $\displaystyle {\frac{E^2+B^2}{c}}$
(ii) Speed of EM wave in vacuum depends on:
(a) Frequency (b) Intensity (c) Wavelength (d) Universal constants $\displaystyle {\mu_0, \varepsilon_0}$
(iii) Displacement current exists in a capacitor during charging when:
(a) Electric field is constant (b) Electric field is changing (c) Magnetic field is constant
(i) (a) $\displaystyle {u = \frac{1}{2}\varepsilon_0 E_{\text{rms}}^2 + \frac{B_{\text{rms}}^2}{2\mu_0} = \frac{1}{2}\varepsilon_0 E_0^2 = \frac{B_0^2}{2\mu_0}}$.
(ii) (d) Universal constants ($\displaystyle {c = 1/\sqrt{\mu_0 \varepsilon_0} \approx 3 \times 10^8\text{ m/s}}$ for all frequencies).
(iii) (b) Electric field is changing ($\displaystyle {dE/dt \neq 0}$).
SECTION E (15 Marks)
Q.31. (a) Write the generalized Ampere-Maxwell circuital law and explain its significance.
(b) Draw a sketch of linearly polarized EM waves propagating in the $\displaystyle {+Z}$ direction, indicating $\displaystyle {\vec{E}}$ and $\displaystyle {\vec{B}}$ directions.
(c) Give one example each of a situation with: (1) displacement current but no conduction current, (2) conduction current but no displacement current.
(a) Why are microwaves suitable for radar navigation?
(b) Why are IR waves called heat waves?
(c) Explain how EM waves transport momentum.
(a) $\displaystyle {\oint \vec{B} \cdot d\vec{l} = \mu_0 \left(I_c + \varepsilon_0 {\frac{{d\Phi_E}}{{dt}}}\right)}$. Significance: Establishes current continuity across capacitor gaps and predicts EM wave propagation.
(b) If wave propagates along $\displaystyle {+Z}$: $\displaystyle {\vec{E} = E_0 \sin(k z - \omega t) \hat{i}}$ (along X) and $\displaystyle {\vec{B} = B_0 \sin(k z - \omega t) \hat{j}}$ (along Y).
(c) (1) Between plates of a charging capacitor ($\displaystyle {I_c = 0, I_d \neq 0}$), (2) Inside a copper wire carrying steady DC ($\displaystyle {I_c \neq 0, I_d = 0}$).
Q.32. A parallel plate capacitor of circular plates with radius $\displaystyle {R = 6.0\text{ cm}}$ has capacitance $\displaystyle {C = 100\text{ pF}}$. It is connected to a $\displaystyle {230\text{ V AC}}$ supply with angular frequency $\displaystyle {\omega = 300\text{ rad/s}}$.
(i) Calculate the RMS value of conduction current.
(ii) Is conduction current equal to displacement current?
(iii) Determine the amplitude of magnetic field $\displaystyle {B}$ at a point $\displaystyle {r = 3.0\text{ cm}}$ from the central axis between the plates.
(i) $\displaystyle {V_{\text{rms}} = 230\text{ V}, \omega = 300\text{ rad/s}, C = 100 \times 10^{-12}\text{ F}}$.
Capacitive Reactance: $\displaystyle {X_C = {\frac{{1}}{{\omega C}}} = {\frac{{1}}{{300 \times 100 \times 10^{-12}}}} = {\frac{{10^8}}{{3}}\,\Omega}}$.
RMS Current: $\displaystyle {I_{\text{rms}} = {\frac{{V_{\text{rms}}}{{X_C}}} = 230 \times (3 \times 10^{-8}) = 6.9 \times 10^{-6}\text{ A} = 6.9\,\mu\text{A}}$.
(ii) Yes, $\displaystyle {I_c = I_d = 6.9\,\mu\text{A}}$ at all times, maintaining circuit continuity.
(iii) Peak Current $\displaystyle {I_0 = \sqrt{2} I_{\text{rms}} = 1.414 \times 6.9\,\mu\text{A} \approx 9.76\,\mu\text{A}}$.
Magnetic field amplitude at $\displaystyle {r = 3\text{ cm}}$ ($\displaystyle {r < R = 6\text{ cm}}$):
$\displaystyle {B_0 = {\frac{{\mu_0 I_0 r}}{{2\pi R^2}}} = {\frac{{(4\pi \times 10^{-7}) \times (9.76 \times 10^{-6}) \times 0.03}}{{2\pi \times (0.06)^2}}} = 4.6 \times 10^{-11}\text{ T}}$.
Q.33. (a) Derive expression for speed of light $\displaystyle {c = 1/\sqrt{\mu_0 \varepsilon_0}}$ using Maxwell's field equations.
(b) The magnetic field amplitude of a floodlight beam is $\displaystyle {B_0 = 12 \times 10^{-8}\text{ T}}$. Find the average intensity of the beam in vacuum.
(b) Average Intensity $\displaystyle {I = u \cdot c = \left({\frac{{B_0^2}}{{2\mu_0}}}\right) c = {\frac{{(12 \times 10^{-8})^2 \times (3 \times 10^8)}}{{2 \times (4\pi \times 10^{-7})}}} = {\frac{{1.44 \times 10^{-14} \times 3 \times 10^8}}{{8\pi \times 10^{-7}}}} = {\frac{{4.32 \times 10^{-6}}}{{2.513 \times 10^{-6}}}} \approx 1.72\text{ W/m}^2}$.
ASSIGNMENT – 2 (MCQ PRACTICE)
1. To dissociate an oxygen molecule into two oxygen atoms, $\displaystyle {5\text{ eV}}$ of energy is required. The minimum frequency of radiation belongs to:
Explanation: $\displaystyle {E = h\nu \implies \nu = {\frac{{5 \times 1.6 \times 10^{-19}}}{{6.63 \times 10^{-34}}}} \approx 1.2 \times 10^{15}\text{ Hz}}$, which falls in the Ultraviolet band.
2. Welder's protective goggles protect eyes primarily from harmful:
3. An EM wave of frequency $\displaystyle {3\text{ kHz}}$ passes from vacuum into glass. The ratio of its frequency in vacuum to glass is:
Explanation: Frequency is determined solely by the wave source and remains unchanged ($\displaystyle {1:1}$) when transitioning between media.
4. Ratio of amplitudes of electric and magnetic field vectors in free space ($\displaystyle {E_0 / B_0}$) is equal to:
5. Which electromagnetic wave is utilized in remote-control devices like TV remotes?
ASSIGNMENT – 3 (ASSERTION & REASON)
1. Assertion (A): Electromagnetic waves do not require any material medium for propagation.
Reason (R): EM waves consist of self-sustaining oscillating electric and magnetic fields regenerating each other in vacuum.
2. Assertion (A): Speed of EM waves in vacuum is given by $\displaystyle {1/\sqrt{\mu_0 \varepsilon_0}}$.
Reason (R): Universal constants $\displaystyle {\mu_0}$ and $\displaystyle {\varepsilon_0}$ define the magnetic and electric properties of free space.
3. Assertion (A): X-rays are widely used to detect fractures in bones.
Reason (R): X-rays pass through soft body tissues easily but are absorbed by dense bones, producing high contrast shadowgraphs.
ASSIGNMENT – 4 (CASE STUDY QUESTIONS)
Case Study: Solar Radiation & Atmospheric Absorption
Solar radiation consists of a continuous EM spectrum including UV, Visible, and IR rays.
1. Solar radiation is fundamentally: (a) Transverse EM wave (b) Longitudinal wave
2. Biological importance of stratospheric ozone layer: (a) Stops UV rays (b) Reduces greenhouse effect
3. All EM waves in vacuum travel at speed: (a) $\displaystyle {3 \times 10^8\text{ m/s}}$ (b) $\displaystyle {3 \times 10^6\text{ m/s}}$
ASSIGNMENT – 5 (FORMULAE & CONCEPTUAL QUESTIONS)
CORE FORMULAE SUMMARY
$\displaystyle {I_d = \varepsilon_0 {\frac{{d\Phi_E}}{{dt}}}}$ | Ampere-Maxwell Law: $\displaystyle {\oint \vec{B} \cdot d\vec{l} = \mu_0 \left(I_c + \varepsilon_0 {\frac{{d\Phi_E}}{{dt}}}\right)}$
Average Energy Density: $\displaystyle {u = u_E + u_B = {\frac{{1}}{{2}}} \varepsilon_0 E_0^2 = {\frac{{B_0^2}}{{2\mu_0}}}}$ | Intensity: $\displaystyle {I = u \cdot c = {\frac{{1}}{{2}}} \varepsilon_0 E_0^2 c}$
CONCEPTUAL SHORT QUESTIONS
1. Why does a microwave oven heat food containing water molecules most efficiently?
2. A variable frequency AC source is connected across a capacitor. How does displacement current change when frequency decreases?
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