Question 3 of 8beginner💡 UnderstandShort Answer2 marks

A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?

Correct Answer

For a plane electromagnetic wave traveling along the z-direction, the electric field and magnetic field vectors are perpendicular to each other and also perpendicular to the direction of propagation. If the wave propagates along the z-axis, the electric field oscillates along the x-axis and the magnetic field oscillates along the y-axis.

For the wavelength calculation:

  • Frequency (ν) = 30 MHz = 30×30 \times 10^{6}$$ Hz
  • Speed of light (c) = 3×3 \times 10^{8}$$ m/s
  • Using the relation c = νλ
  • Wavelength (λ) = c/ν = (3×3 \times 10^{8} )/(30×30 \times 10^{6}$$) = 10 m
Exercise: EXERCISES | Q: 8.4
For More Understanding

Explanation

The textbook context states that for an electromagnetic wave propagating along the z-direction, the electric field Ex is along the x-axis and the magnetic field By is along the y-axis. Both fields are perpendicular to each other and to the direction of propagation. For the numerical calculation, using the fundamental relation c = νλ where c is the speed of light (3×3 \times 10^{8} m/s, given in context) and ν is the frequency (30 MHz = 30×30 \times 10^{6}$$ Hz), the wavelength is calculated as λ = c/ν = 10 m.

Solution Steps

  1. Step 1: State that E and B fields are perpendicular to each other and to the propagation direction (z-axis)

  2. Step 2: Convert frequency: ν = 30 MHz = 30×30 \times 10^{6}$$ Hz

  3. Step 3: Apply wavelength formula: λ = c/ν

  4. Step 4: Calculate: λ = (3×3 \times 10^{8} )/(30×30 \times 10^{6}$$) = 10 m

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