Electromagnetic Waves Problems

This section provides 100 problems to test your understanding of electromagnetic waves, including calculations of wave speed, wavelength, frequency, intensity, and energy density, as well as properties like polarization and the electromagnetic spectrum. Inspired by JEE Main, JEE Advanced, and NEET exam patterns, these problems are tailored for exam preparation, offering a mix of numerical, conceptual, and derivation-based challenges. NEET-style problems (66–100) are formatted as multiple-choice questions (MCQs) to match the exam’s objective format. Problems are organized by type to support progressive learning and build confidence in mastering electromagnetism, a key topic for JEE/NEET success.

Numerical Problems

1. Calculate the speed of an electromagnetic wave in vacuum given ${\mu }_0=4\pi \times {10}^{-7}\text{H/m}$ and ${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/({\text{N·m}}^2)$.

   • (a) $2.99\times {10}^8\text{m/s}$
   • (b) $3.00\times {10}^8\text{m/s}$
   • (c) $3.01\times {10}^8\text{m/s}$
   • (d) $3.02\times {10}^8\text{m/s}$

2. An electromagnetic wave has a frequency $f=5\times {10}^6\text{Hz}$. Calculate its wavelength $\lambda$ in vacuum ($c=3\times {10}^8\text{m/s}$).

   • (a) $59.9\text{m}$
   • (b) $60.0\text{m}$
   • (c) $60.1\text{m}$
   • (d) $60.2\text{m}$

3. An electromagnetic wave has a wavelength $\lambda =400\text{nm}$. Calculate its frequency $f$ in vacuum.

   • (a) $7.49\times {10}^{14}\text{Hz}$
   • (b) $7.50\times {10}^{14}\text{Hz}$
   • (c) $7.51\times {10}^{14}\text{Hz}$
   • (d) $7.52\times {10}^{14}\text{Hz}$

4. An electromagnetic wave has an electric field amplitude $E_0=50\text{V/m}$. Calculate the magnetic field amplitude $B_0$.

   • (a) $1.66\times {10}^{-7}\text{T}$
   • (b) $1.67\times {10}^{-7}\text{T}$
   • (c) $1.68\times {10}^{-7}\text{T}$
   • (d) $1.69\times {10}^{-7}\text{T}$

5. An electromagnetic wave has a wave number $k=2\times {10}^6{\text{m}}^{-1}$. Calculate its wavelength $\lambda$.

   • (a) $3.14\times {10}^{-6}\text{m}$
   • (b) $3.15\times {10}^{-6}\text{m}$
   • (c) $3.16\times {10}^{-6}\text{m}$
   • (d) $3.17\times {10}^{-6}\text{m}$

6. An electromagnetic wave has an angular frequency $\omega =4\times {10}^{15}\text{rad/s}$. Calculate its frequency $f$.

   • (a) $6.36\times {10}^{14}\text{Hz}$
   • (b) $6.37\times {10}^{14}\text{Hz}$
   • (c) $6.38\times {10}^{14}\text{Hz}$
   • (d) $6.39\times {10}^{14}\text{Hz}$

7. An electromagnetic wave has $E_0=120\text{V/m}$. Calculate the average intensity $I$ (${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/({\text{N·m}}^2)$).

   • (a) $19.1{\text{W/m}}^2$
   • (b) $19.2{\text{W/m}}^2$
   • (c) $19.3{\text{W/m}}^2$
   • (d) $19.4{\text{W/m}}^2$

8. An electromagnetic wave has $B_0=3\times {10}^{-7}\text{T}$. Calculate $E_0$.

   • (a) $89.9\text{V/m}$
   • (b) $90.0\text{V/m}$
   • (c) $90.1\text{V/m}$
   • (d) $90.2\text{V/m}$

9. An electromagnetic wave has $I=10{\text{W/m}}^2$. Calculate $E_0$.

   • (a) $86.6\text{V/m}$
   • (b) $86.7\text{V/m}$
   • (c) $86.8\text{V/m}$
   • (d) $86.9\text{V/m}$

10. An electromagnetic wave has $E_0=80\text{V/m}$. Calculate the average energy density $u_{\text{avg}}$.

    • (a) $2.83\times {10}^{-8}{\text{J/m}}^3$
    • (b) $2.84\times {10}^{-8}{\text{J/m}}^3$
    • (c) $2.85\times {10}^{-8}{\text{J/m}}^3$
    • (d) $2.86\times {10}^{-8}{\text{J/m}}^3$

11. An electromagnetic wave has $\lambda =500\text{nm}$. Calculate $k$.

    • (a) $1.25\times {10}^7{\text{m}}^{-1}$
    • (b) $1.26\times {10}^7{\text{m}}^{-1}$
    • (c) $1.27\times {10}^7{\text{m}}^{-1}$
    • (d) $1.28\times {10}^7{\text{m}}^{-1}$

12. An electromagnetic wave has $f={10}^{12}\text{Hz}$. Calculate $\lambda$.

    • (a) $2.99\times {10}^{-4}\text{m}$
    • (b) $3.00\times {10}^{-4}\text{m}$
    • (c) $3.01\times {10}^{-4}\text{m}$
    • (d) $3.02\times {10}^{-4}\text{m}$

13. An electromagnetic wave has $E_0=200\text{V/m}$. Calculate $I$.

    • (a) $53.0{\text{W/m}}^2$
    • (b) $53.1{\text{W/m}}^2$
    • (c) $53.2{\text{W/m}}^2$
    • (d) $53.3{\text{W/m}}^2$

14. An electromagnetic wave has $B_0=1\times {10}^{-7}\text{T}$. Calculate $u_{\text{avg}}$.

    • (a) $8.85\times {10}^{-9}{\text{J/m}}^3$
    • (b) $8.86\times {10}^{-9}{\text{J/m}}^3$
    • (c) $8.87\times {10}^{-9}{\text{J/m}}^3$
    • (d) $8.88\times {10}^{-9}{\text{J/m}}^3$

15. An electromagnetic wave has $f=3\times {10}^{15}\text{Hz}$. Calculate $\omega$.

    • (a) $1.88\times {10}^{16}\text{rad/s}$
    • (b) $1.89\times {10}^{16}\text{rad/s}$
    • (c) $1.90\times {10}^{16}\text{rad/s}$
    • (d) $1.91\times {10}^{16}\text{rad/s}$

16. An electromagnetic wave has $\lambda =200\text{nm}$. Calculate $f$.

    • (a) $1.49\times {10}^{15}\text{Hz}$
    • (b) $1.50\times {10}^{15}\text{Hz}$
    • (c) $1.51\times {10}^{15}\text{Hz}$
    • (d) $1.52\times {10}^{15}\text{Hz}$

17. An electromagnetic wave has $I=30{\text{W/m}}^2$. Calculate $B_0$.

    • (a) $1.58\times {10}^{-7}\text{T}$
    • (b) $1.59\times {10}^{-7}\text{T}$
    • (c) $1.60\times {10}^{-7}\text{T}$
    • (d) $1.61\times {10}^{-7}\text{T}$

18. An electromagnetic wave has $E_0=60\text{V/m}$. Calculate $u_{\text{avg}}$.

    • (a) $1.59\times {10}^{-8}{\text{J/m}}^3$
    • (b) $1.60\times {10}^{-8}{\text{J/m}}^3$
    • (c) $1.61\times {10}^{-8}{\text{J/m}}^3$
    • (d) $1.62\times {10}^{-8}{\text{J/m}}^3$

19. An electromagnetic wave has $k=5\times {10}^6{\text{m}}^{-1}$. Calculate $\omega$.

    • (a) $1.49\times {10}^{15}\text{rad/s}$
    • (b) $1.50\times {10}^{15}\text{rad/s}$
    • (c) $1.51\times {10}^{15}\text{rad/s}$
    • (d) $1.52\times {10}^{15}\text{rad/s}$

20. An electromagnetic wave has $\lambda =600\text{nm}$. Calculate $k$.

    • (a) $1.04\times {10}^7{\text{m}}^{-1}$
    • (b) $1.05\times {10}^7{\text{m}}^{-1}$
    • (c) $1.06\times {10}^7{\text{m}}^{-1}$
    • (d) $1.07\times {10}^7{\text{m}}^{-1}$

21. An electromagnetic wave has $f={10}^{18}\text{Hz}$. Calculate $\lambda$.

    • (a) $2.99\times {10}^{-10}\text{m}$
    • (b) $3.00\times {10}^{-10}\text{m}$
    • (c) $3.01\times {10}^{-10}\text{m}$
    • (d) $3.02\times {10}^{-10}\text{m}$

22. An electromagnetic wave has $E_0=300\text{V/m}$. Calculate $I$.

    • (a) $119.4{\text{W/m}}^2$
    • (b) $119.5{\text{W/m}}^2$
    • (c) $119.6{\text{W/m}}^2$
    • (d) $119.7{\text{W/m}}^2$

23. An electromagnetic wave has $B_0=5\times {10}^{-7}\text{T}$. Calculate $E_0$.

    • (a) $149.9\text{V/m}$
    • (b) $150.0\text{V/m}$
    • (c) $150.1\text{V/m}$
    • (d) $150.2\text{V/m}$

24. An electromagnetic wave has $I=50{\text{W/m}}^2$. Calculate $E_0$.

    • (a) $193.5\text{V/m}$
    • (b) $193.6\text{V/m}$
    • (c) $193.7\text{V/m}$
    • (d) $193.8\text{V/m}$

25. An electromagnetic wave has $E_0=40\text{V/m}$. Calculate $u_{\text{avg}}$.

    • (a) $7.07\times {10}^{-9}{\text{J/m}}^3$
    • (b) $7.08\times {10}^{-9}{\text{J/m}}^3$
    • (c) $7.09\times {10}^{-9}{\text{J/m}}^3$
    • (d) $7.10\times {10}^{-9}{\text{J/m}}^3$

26. An electromagnetic wave has $\omega =2\times {10}^{16}\text{rad/s}$. Calculate $f$.

    • (a) $3.18\times {10}^{15}\text{Hz}$
    • (b) $3.19\times {10}^{15}\text{Hz}$
    • (c) $3.20\times {10}^{15}\text{Hz}$
    • (d) $3.21\times {10}^{15}\text{Hz}$

27. An electromagnetic wave has $\lambda =100\text{nm}$. Calculate $f$.

    • (a) $2.99\times {10}^{15}\text{Hz}$
    • (b) $3.00\times {10}^{15}\text{Hz}$
    • (c) $3.01\times {10}^{15}\text{Hz}$
    • (d) $3.02\times {10}^{15}\text{Hz}$

28. An electromagnetic wave has $k=1\times {10}^7{\text{m}}^{-1}$. Calculate $\lambda$.

    • (a) $6.28\times {10}^{-7}\text{m}$
    • (b) $6.29\times {10}^{-7}\text{m}$
    • (c) $6.30\times {10}^{-7}\text{m}$
    • (d) $6.31\times {10}^{-7}\text{m}$

29. An electromagnetic wave has $f={10}^{16}\text{Hz}$. Calculate $\omega$.

    • (a) $6.28\times {10}^{16}\text{rad/s}$
    • (b) $6.29\times {10}^{16}\text{rad/s}$
    • (c) $6.30\times {10}^{16}\text{rad/s}$
    • (d) $6.31\times {10}^{16}\text{rad/s}$

30. An electromagnetic wave has $E_0=250\text{V/m}$. Calculate $I$.

    • (a) $82.9{\text{W/m}}^2$
    • (b) $83.0{\text{W/m}}^2$
    • (c) $83.1{\text{W/m}}^2$
    • (d) $83.2{\text{W/m}}^2$

31. A spacecraft uses a radio wave with $f=2\times {10}^8\text{Hz}$ for communication. Calculate $\lambda$.

    • (a) $1.49\text{m}$
    • (b) $1.50\text{m}$
    • (c) $1.51\text{m}$
    • (d) $1.52\text{m}$

32. An electromagnetic wave has $I=100{\text{W/m}}^2$. Calculate $B_0$.

    • (a) $2.89\times {10}^{-7}\text{T}$
    • (b) $2.90\times {10}^{-7}\text{T}$
    • (c) $2.91\times {10}^{-7}\text{T}$
    • (d) $2.92\times {10}^{-7}\text{T}$

33. An electromagnetic wave has $\lambda =800\text{nm}$. Calculate $k$.

    • (a) $7.85\times {10}^6{\text{m}}^{-1}$
    • (b) $7.86\times {10}^6{\text{m}}^{-1}$
    • (c) $7.87\times {10}^6{\text{m}}^{-1}$
    • (d) $7.88\times {10}^6{\text{m}}^{-1}$

34. An electromagnetic wave has $B_0=4\times {10}^{-7}\text{T}$. Calculate $u_{\text{avg}}$.

    • (a) $3.53\times {10}^{-8}{\text{J/m}}^3$
    • (b) $3.54\times {10}^{-8}{\text{J/m}}^3$
    • (c) $3.55\times {10}^{-8}{\text{J/m}}^3$
    • (d) $3.56\times {10}^{-8}{\text{J/m}}^3$

35. An electromagnetic wave has $f={10}^{14}\text{Hz}$. Calculate $\lambda$.

    • (a) $2.99\times {10}^{-6}\text{m}$
    • (b) $3.00\times {10}^{-6}\text{m}$
    • (c) $3.01\times {10}^{-6}\text{m}$
    • (d) $3.02\times {10}^{-6}\text{m}$

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Conceptual Problems

36. What produces electromagnetic waves according to Maxwell’s equations?

• (a) Static charges
• (b) Accelerating charges
• (c) Constant magnetic fields
• (d) Static electric fields

37. What is the nature of electromagnetic waves?

• (a) Longitudinal
• (b) Transverse
• (c) Stationary
• (d) Scalar

38. What is the unit of intensity of an electromagnetic wave in SI units?

• (a) W/m²
• (b) J/m³
• (c) V/m
• (d) T

39. What happens to the wavelength of an electromagnetic wave as its frequency increases?

• (a) Increases
• (b) Decreases
• (c) Remains constant
• (d) Becomes infinite

40. What does the electromagnetic spectrum include?

• (a) Only visible light
• (b) Radio waves to gamma rays
• (c) Only infrared waves
• (d) Only ultraviolet waves

41. What is the unit of wave number $k$ in SI units?

• (a) m
• (b) m⁻¹
• (c) rad/s
• (d) Hz

42. What does the Poynting vector $\overrightarrow{S}$ represent?

• (a) Energy density
• (b) Electric field strength
• (c) Energy flux
• (d) Magnetic field strength

43. What happens to the speed of an electromagnetic wave in a medium compared to vacuum?

• (a) Increases
• (b) Decreases
• (c) Remains the same
• (d) Becomes zero

44. What does a frequency of ${10}^{15}\text{Hz}$ indicate in the electromagnetic spectrum?

• (a) Radio wave
• (b) Microwave
• (c) Ultraviolet
• (d) Gamma ray

45. What is the dimension of energy density $u$?

• (a) $[\text{M}{\text{L}}^{-1}{\text{T}}^{-2}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

46. What does a zero Poynting vector indicate?

• (a) No energy transport
• (b) Maximum energy transport
• (c) No electric field
• (d) No magnetic field

47. What is the significance of $\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$?

• (a) Wavelength of an electromagnetic wave
• (b) Speed of light in vacuum
• (c) Intensity of the wave
• (d) Energy density

48. What happens to the intensity of an electromagnetic wave if $E_0$ doubles?

• (a) Doubles
• (b) Quadruples
• (c) Halves
• (d) Remains the same

49. What does the polarization of an electromagnetic wave describe?

• (a) Direction of propagation
• (b) Direction of the electric field
• (c) Speed of the wave
• (d) Frequency of the wave

50. How do electromagnetic waves assist in spacecraft communication?

• (a) Increase resistance
• (b) Enable signal transmission via radio waves
• (c) Reduce frequency
• (d) Increase energy density

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Derivation Problems

51. Derive the wave equation for an electromagnetic wave ${\mathrm{\nabla }}^2\overrightarrow{E}={\mu }_0{ϵ}_0\frac{{\partial }^2\overrightarrow{E}}{\partial t^2}$.

52. Derive the relationship between $E_0$ and $B_0$ in an electromagnetic wave $E_0=c{B}_0$.

53. Derive the average intensity of an electromagnetic wave $I=\frac{1}{2}{ϵ}_{0}c{E}_0^2$.

54. Derive the energy density of an electromagnetic wave $u={ϵ}_0{E}^2$.

55. Derive the Poynting vector for a plane electromagnetic wave $\overrightarrow{S}=\frac{1}{{\mu }_0}\overrightarrow{E}\times \overrightarrow{B}$.

56. Derive the wave number $k$ for a wave with wavelength $\lambda$, $k=\frac{2\pi }{\lambda }$.

57. Derive the angular frequency $\omega$ for a wave with frequency $f$, $\omega =2\pi f$.

58. Derive the speed of an electromagnetic wave in vacuum $c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$.

59. Derive the relationship between frequency $f$ and wavelength $\lambda$, $f\lambda =c$.

60. Derive the average energy density using $B_0$, $u_{\text{avg}}=\frac{1}{2}\frac{B_{\text{rms}}^2}{{\mu }_0}$.

61. Derive the electric field amplitude $E_0$ from intensity $I$, $E_0=\sqrt{\frac{2I}{{ϵ}_{0}c}}$.

62. Derive the magnetic field amplitude $B_0$ from intensity $I$, $B_0=\sqrt{\frac{2I{\mu }_0}{c}}$.

63. Derive the wavelength of a visible light wave with a given frequency.

64. Derive the frequency of an X-ray with a given wavelength.

65. Derive the polarization direction of a plane electromagnetic wave.

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NEET-style Conceptual Problems

66. What is the unit of angular frequency $\omega$ in SI units?

• (a) Hz
• (b) rad/s
• (c) m⁻¹
• (d) W/m²

67. What does a changing electric field produce in an electromagnetic wave?

• (a) Static electric field
• (b) Changing magnetic field
• (c) No field
• (d) Static magnetic field

68. What is the relationship between $E_0$ and $B_0$ in an electromagnetic wave?

• (a) $E_0=B_0$
• (b) $E_0=c{B}_0$
• (c) $E_0=\frac{B_0}{c}$
• (d) $E_0$ is independent of $B_0$

69. What happens to the speed of an electromagnetic wave in vacuum?

• (a) Depends on frequency
• (b) Depends on wavelength
• (c) Remains constant at $c$
• (d) Becomes zero

70. What is the dimension of the Poynting vector $\overrightarrow{S}$?

• (a) $[\text{M}{\text{T}}^{-3}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

71. What does the frequency of an electromagnetic wave determine?

• (a) Speed of the wave
• (b) Position in the electromagnetic spectrum
• (c) Energy density
• (d) Polarization

72. What is the role of Maxwell’s equations in electromagnetic waves?

• (a) Predict static fields
• (b) Predict wave propagation
• (c) Reduce energy transport
• (d) Increase wavelength

73. What happens to the intensity of an electromagnetic wave if $B_0$ doubles?

• (a) Doubles
• (b) Quadruples
• (c) Halves
• (d) Remains the same

74. Why does visible light have a frequency range of $4\times {10}^{14}$–$7.5\times {10}^{14}\text{Hz}$?

• (a) Due to its wavelength range
• (b) Due to its speed
• (c) Due to its intensity
• (d) Due to its polarization

75. What is the unit of energy density $u$?

• (a) J/m³
• (b) W/m²
• (c) V/m
• (d) T

76. What does a constant intensity of an electromagnetic wave indicate?

• (a) Changing $E_0$
• (b) Constant $E_0$
• (c) No wave propagation
• (d) No energy transport

77. Which type of wave is used for long-range communication in spacecraft?

• (a) Gamma ray
• (b) X-ray
• (c) Radio wave
• (d) Ultraviolet wave

78. What is the direction of $\overrightarrow{E}$ and $\overrightarrow{B}$ in an electromagnetic wave?

• (a) Parallel to each other
• (b) Perpendicular to each other
• (c) Random
• (d) Along the propagation direction

79. What does a pseudo-force do in a non-inertial frame for electromagnetic wave calculations?

• (a) Affects perceived wave speed
• (b) Affects charge distribution
• (c) Creates waves
• (d) Reduces intensity

80. What is the dimension of $E_0/B_0$?

• (a) $[\text{L}{\text{T}}^{-1}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

81. What is the role of radio waves in spacecraft navigation?

• (a) Increase intensity
• (b) Enable long-range communication
• (c) Reduce wavelength
• (d) Increase energy density

82. What happens to the energy density if $E_0$ doubles?

• (a) Doubles
• (b) Quadruples
• (c) Halves
• (d) Remains the same

83. Why does the intensity of an electromagnetic wave depend on $E_0^2$?

• (a) Due to $I=\frac{1}{2}{ϵ}_{0}c{E}_0^2$
• (b) Due to increased wavelength
• (c) Due to decreased frequency
• (d) Due to static fields

84. What is the significance of $\frac{2\pi }{\lambda }$?

• (a) Angular frequency
• (b) Wave number
• (c) Intensity
• (d) Energy density

85. What is the unit of $E_0$ in an electromagnetic wave?

• (a) V/m
• (b) T
• (c) A/m
• (d) W/m²

86. What does a frequency of ${10}^{20}\text{Hz}$ indicate in the spectrum?

• (a) Radio wave
• (b) Microwave
• (c) Visible light
• (d) Gamma ray

87. What is the physical significance of ${ϵ}_{0}c{E}_0^2$?

• (a) Wave number
• (b) Intensity of the wave
• (c) Speed of the wave
• (d) Wavelength

88. Why does the speed of an electromagnetic wave in vacuum not depend on frequency?

• (a) Due to $c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$
• (b) Due to polarization
• (c) Due to intensity
• (d) Due to energy density

89. What is the dimension of $\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$?

• (a) $[\text{L}{\text{T}}^{-1}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

90. How does the electromagnetic spectrum assist in spacecraft imaging?

• (a) Increases intensity
• (b) Uses infrared for thermal imaging
• (c) Reduces frequency
• (d) Increases wavelength

91. What is the role of wavelength in the electromagnetic spectrum?

• (a) Determines the speed
• (b) Determines the position in the spectrum
• (c) Determines the intensity
• (d) Determines the polarization

92. What does a high intensity of an electromagnetic wave indicate?

• (a) Low $E_0$
• (b) High $E_0$
• (c) No wave propagation
• (d) No energy transport

93. What is the physical significance of $2\pi f$?

• (a) Wave number
• (b) Angular frequency
• (c) Intensity
• (d) Energy density

94. What is the dimension of $E_0\times B_0$?

• (a) $[\text{M}{\text{T}}^{-3}]$
• (b) $[\text{M}\text{L}{\text{T}}^{-1}]$
• (c) $[\text{L}{\text{T}}^{-2}]$
• (d) $[\text{M}{\text{L}}^2{\text{T}}^{-1}]$

95. Why does the energy density of an electromagnetic wave depend on $E^2$?

• (a) Due to $u={ϵ}_0{E}^2$
• (b) Due to increased wavelength
• (c) Due to decreased frequency
• (d) Due to static fields

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NEET-style Numerical Problems

96. An electromagnetic wave has $f={10}^7\text{Hz}$. Calculate $\lambda$.

• (a) $29.9\text{m}$
• (b) $30.0\text{m}$
• (c) $30.1\text{m}$
• (d) $30.2\text{m}$

97. An electromagnetic wave has $E_0=150\text{V/m}$. Calculate $B_0$.

• (a) $4.99\times {10}^{-7}\text{T}$
• (b) $5.00\times {10}^{-7}\text{T}$
• (c) $5.01\times {10}^{-7}\text{T}$
• (d) $5.02\times {10}^{-7}\text{T}$

98. An electromagnetic wave has $\lambda =700\text{nm}$. Calculate $f$.

• (a) $4.28\times {10}^{14}\text{Hz}$
• (b) $4.29\times {10}^{14}\text{Hz}$
• (c) $4.30\times {10}^{14}\text{Hz}$
• (d) $4.31\times {10}^{14}\text{Hz}$

99. An electromagnetic wave has $I=25{\text{W/m}}^2$. Calculate $E_0$.

• (a) $137.0\text{V/m}$
• (b) $137.1\text{V/m}$
• (c) $137.2\text{V/m}$
• (d) $137.3\text{V/m}$

100. An electromagnetic wave has $E_0=100\text{V/m}$. Calculate $u_{\text{avg}}$.
     - (a) $4.42\times {10}^{-8}{\text{J/m}}^3$
     - (b) $4.43\times {10}^{-8}{\text{J/m}}^3$
     - (c) $4.44\times {10}^{-8}{\text{J/m}}^3$
     - (d) $4.45\times {10}^{-8}{\text{J/m}}^3$

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