Contents
Chapter 8: 60-Question Marathon
Complete all 5 levels to master Electromagnetic Waves.
Level 1: The Basics (1-12)
Warm Up
1. Who theoretically predicted the existence of electromagnetic waves?
Maxwell.
2. Who experimentally verified the existence of EM waves?
Heinrich Hertz.
3. What is the source of electromagnetic waves?
Accelerated charge. (Oscillating charge).
4. Are EM waves mechanical or non-mechanical?
Non-mechanical. They do not require a material medium to propagate.
5. What is the speed of EM waves in vacuum?
$c = 3 \times 10^8 m/s$.
6. Write the expression for the speed of EM waves in terms of permeability and permittivity.
$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$.
7. What is the nature of EM waves (Longitudinal or Transverse)?
Transverse. (Electric and Magnetic fields are perpendicular to direction of propagation).
8. What is the angle between Electric field ($\vec{E}$) and Magnetic field ($\vec{B}$) in an EM wave?
$90^\circ$ ($\pi/2$ radians).
9. What is the phase difference between $\vec{E}$ and $\vec{B}$?
Zero. They oscillate in the same phase.
10. Do EM waves carry energy?
Yes, they carry both energy and momentum.
11. Which vector represents the direction of propagation of the EM wave?
The vector $\vec{E} \times \vec{B}$ (Poynting vector).
12. What is Displacement Current ($I_d$)?
It is the current which comes into play in a region where the electric field (or electric flux) is changing with time. $I_d = \epsilon_0 \frac{d\phi_E}{dt}$.
Level 2: The Spectrum (13-30)
High Probability
💡 Exam Tip: Questions on "Uses" are the most repeated in CBSE history. Memorize these carefully!
13. Arrange the following in increasing order of frequency: Microwaves, Gamma rays, UV rays, Radiowaves.
Radiowaves < Microwaves < UV rays < Gamma rays.
14. Which waves are used in Radar systems for aircraft navigation?
Microwaves.
15. Which waves are used in optical fiber communication?
Visible light (or Near Infrared).
16. Which rays are used in LASIK eye surgery?
Ultraviolet (UV) rays.
17. Which EM waves are detected by the ozone layer?
Ultraviolet (UV) rays.
18. Which waves are used in remote switches of household electronic systems?
Infrared (IR) rays.
19. Which waves are used for studying crystal structure?
X-rays.
20. Which waves are produced by radioactive decay of the nucleus?
Gamma rays.
21. Which waves are often called "Heat Waves"?
Infrared waves.
22. Name the EM wave used for water purification.
Ultraviolet (UV) rays (to kill germs).
23. What are the waves used in cellular phones?
Radio waves (UHF/VHF bands).
24. Which waves are used in checking for fractures in bones?
X-rays.
25. Which wave has the longest wavelength?
Radio waves.
26. Which wave has the highest penetrating power?
Gamma rays.
27. How are X-rays produced?
By bombarding a high atomic weight metal target with high-energy electrons.
28. Name the wave used in microwave ovens.
Microwaves (frequency matches resonant frequency of water molecules).
29. Which waves are used to treat cancer?
Gamma rays (Radiotherapy).
30. Identify the wave: $\lambda \approx 10^{-10} m$.
X-rays.
Level 3: Reasoning (31-45)
Brain Teasers
31. Can a static electric field produce a magnetic field?
No. Only a changing electric field or a moving charge produces a magnetic field.
32. Why did Maxwell introduce the concept of Displacement Current?
To remove the inconsistency in Ampere’s Circuital Law for circuits containing capacitors (discontinuous current path).
33. The charging current for a capacitor is 0.25 A. What is the displacement current across its plates?
0.25 A. (Inside the capacitor, $I_d = I_{conduction}$).
34. Do EM waves require a medium for propagation? Give reason.
No. They are oscillations of electric and magnetic fields which are properties of space itself, not of a material medium.
35. Why do welders wear special glass goggles?
To protect their eyes from large amounts of harmful UV radiation produced by welding arcs.
36. Why are microwaves used in radar instead of radio waves?
Microwaves have smaller wavelengths, so they spread (diffract) less and can be directed as a narrow beam to detect small objects like aircraft.
37. Is the ratio $E_0/B_0$ constant for all EM waves in vacuum?
Yes, it equals the speed of light ($c$).
38. What physical quantity oscillates in an EM wave?
Electric Field ($\vec{E}$) and Magnetic Field ($\vec{B}$).
39. Why do we not feel the momentum transfer from sunlight?
Because the value of momentum $p = U/c$ is extremely small (since $c$ is very large).
40. What is Radiation Pressure?
The force exerted by electromagnetic waves on a unit area of a surface is called radiation pressure.
41. If the earth did not have an atmosphere, would its average surface temperature be higher or lower?
Lower. The atmosphere (greenhouse gases) traps infrared radiation. Without it, heat would escape.
42. Can sound waves travel in vacuum?
No, sound is mechanical. EM waves are the only waves that can travel in vacuum.
43. In a plane EM wave, the electric field is along the y-axis and magnetic field is along the z-axis. What is the direction of propagation?
Along the x-axis ($\hat{j} \times \hat{k} = \hat{i}$).
44. A charged particle oscillates about its mean equilibrium position with a frequency of $10^9 Hz$. What is the frequency of the EM waves produced?
$10^9 Hz$. The frequency of the wave is equal to the frequency of the oscillating charge.
45. What is the relation between energy density of Electric field ($u_E$) and Magnetic field ($u_B$)?
$u_E = u_B$. The energy is shared equally.
Level 4: Numericals (46-55)
Calculations
46. The amplitude of the magnetic field part of a harmonic EM wave in vacuum is $B_0 = 510 nT$. What is the amplitude of the electric field part?
Use $E_0 = c B_0$.
$E_0 = 3 \times 10^8 \times 510 \times 10^{-9} = 153 V/m$.
$E_0 = 3 \times 10^8 \times 510 \times 10^{-9} = 153 V/m$.
47. Find the frequency of an EM wave of wavelength 30 m.
$\nu = c/\lambda = (3 \times 10^8) / 30 = 10^7 Hz$ (10 MHz).
48. In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $2 \times 10^{10} Hz$ and amplitude 48 V/m. Find the wavelength.
$\lambda = c/\nu = (3 \times 10^8) / (2 \times 10^{10}) = 1.5 \times 10^{-2} m = 1.5 cm$.
49. Calculate the energy of a photon of frequency $5 \times 10^{14} Hz$. (Given $h = 6.63 \times 10^{-34} Js$).
$E = h\nu = 6.63 \times 10^{-34} \times 5 \times 10^{14} = 3.315 \times 10^{-19} J$.
50. The magnetic field in a plane EM wave is given by $B_y = 2 \times 10^{-7} \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t) T$. What is the wavelength?
Compare with standard equation: $k = 0.5 \times 10^3$.
$\lambda = 2\pi/k = 2\pi / 500 = \pi/250 \approx 0.0126 m$.
$\lambda = 2\pi/k = 2\pi / 500 = \pi/250 \approx 0.0126 m$.
51. Using the data from Q50, write the expression for the electric field.
$E_0 = cB_0 = 3 \times 10^8 \times 2 \times 10^{-7} = 60 V/m$.
Wave travels in -x direction. Since B is in Y, E must be in Z.
$E_z = 60 \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t) V/m$.
Wave travels in -x direction. Since B is in Y, E must be in Z.
$E_z = 60 \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t) V/m$.
52. Calculate the peak value of electric field produced by the radiation of a 100W bulb at a distance of 3m (Assume efficiency 2.5% and point source).
1. Power Radiated = $2.5\%$ of 100W = 2.5 W.
2. Intensity $I = P / (4\pi r^2)$.
3. Use $I = \frac{1}{2}\epsilon_0 E_0^2 c$ to find $E_0$.
2. Intensity $I = P / (4\pi r^2)$.
3. Use $I = \frac{1}{2}\epsilon_0 E_0^2 c$ to find $E_0$.
53. An EM wave travels in a medium with relative permeability 1.3 and relative permittivity 2.14. Find the speed of the wave.
$v = c / \sqrt{\mu_r \epsilon_r} = (3 \times 10^8) / \sqrt{1.3 \times 2.14}$.
54. A radio can tune to any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?
For 7.5 MHz: $\lambda = 300/7.5 = 40m$.
For 12 MHz: $\lambda = 300/12 = 25m$.
Range: 25m to 40m.
For 12 MHz: $\lambda = 300/12 = 25m$.
Range: 25m to 40m.
55. What is the momentum delivered to a surface if energy $U$ is totally reflected?
$p = 2U/c$.
Level 5: The Challenger (56-60)
Expert Mode
56. Which part of the EM spectrum has the largest penetrating power and why?
Gamma rays. Because they have the highest frequency and highest energy ($E=h\nu$).
57. Why is the sky blue?
Scattering of light. Shorter wavelengths (Blue/Violet) are scattered more strongly by atmospheric molecules than longer wavelengths (Red) ($Scattering \propto 1/\lambda^4$).
58. What is the condition for a wave to be polarized?
It must be a transverse wave. Longitudinal waves cannot be polarized. This proves light is transverse.
59. Identify the constituent radiation of the electromagnetic spectrum which is emitted by a klystron or magnetron valve.
Microwaves.
60. Final Boss: Prove that the unit of $1/\sqrt{\mu_0 \epsilon_0}$ is velocity.
Unit of $\mu_0 = Tm/A$. Unit of $\epsilon_0 = C^2 / (N m^2)$.
Substitute $T = N/(Am)$ and $C=As$.
Solving this dimensionally gives $[L T^{-1}]$.
Substitute $T = N/(Am)$ and $C=As$.
Solving this dimensionally gives $[L T^{-1}]$.
🎉 Mission Accomplished!
If you reviewed all 60 questions, you are practically guaranteed to score full marks in this chapter.