Question 5 of 8beginner🔧 ApplyNumerical2 marks

The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0 = 510 nT. What is the amplitude of the electric field part of the wave?

Correct Answer

The amplitude of the electric field part of the wave is 153 N/C (or 153 V/m).

Exercise: EXERCISES | Q: 8.7
For More Understanding

Explanation

This question tests the fundamental relationship between electric and magnetic field amplitudes in an electromagnetic wave. From Maxwell's equations, as stated in the textbook context, the magnitudes are related by E₀/B₀ = c, or equivalently B₀ = E₀/c. The student must convert the given magnetic field amplitude from nanotesla to tesla, then apply the formula to find E₀. The speed of light c = 3×103 \times 10⁸ m/s is a standard constant used throughout the chapter.

Solution Steps

  1. Step 1: Identify the relationship between electric and magnetic field amplitudes from Maxwell's equations: E₀/B₀ = c, which gives E₀ = c × B₀

  2. Step 2: Convert the given magnetic field amplitude to SI units: B₀ = 510 nT = 510×10510 \times 10⁻⁹ T

  3. Step 3: Apply the formula using c = 3×103 \times 10⁸ m/s: E₀ = (3×103 \times 10⁸ m/s) × (510×10510 \times 10⁻⁹ T) = 153 N/C

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