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In an electromagnetic wave in free space the root mean square value of the electric field is \( E_{rms} = 6 \mathrm{V/m} \). The peak value of the magnetic field is

1. 2.83 × 10⁻⁸ T
2. 0.70 × 10⁻⁸ T
3. 4.23 × 10⁻⁸ T
4. 1.41 × 10⁻⁸ T

Correct answer: 2.83 × 10⁻⁸ T

Solution

The peak value of the magnetic field is related to the peak value of the electric field by the equation: \( B_0 = \frac{E_0}{c} \), where \( E_0 = \sqrt{2} E_{rms} \) and \( c \) is the speed of light. Substituting \( E_{rms} = 6 \mathrm{V/m} \), \( E_0 = 6\sqrt{2} \), and \( c = 3 \times 10^8 \mathrm{m/s} \), we get \( B_0 = \frac{6\sqrt{2}}{3 \times 10^8} = 2.83 \times 10^{-8} \mathrm{T} \).

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