Field Amplitude Relation
The electric field amplitude of a plane electromagnetic wave travelling in vacuum is measured to be 90 V/m. What is the amplitude of the associated magnetic field component?
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About This Question
- Subject
- physics
- Chapter
- electromagnetic waves
- Topic
- field amplitude relation
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
3.0×10−7 T
For an electromagnetic wave in vacuum the peak electric and magnetic field magnitudes are not independent; they are locked together by the wave speed through E_0 = cB_0. This relation comes straight from Maxwell's equations and ensures that the electric and magnetic energy densities stay equal. Rearranging gives B_0 = E_0/c = 90/(3.0 \times 10^{8}) = 3.0 \times 10^{-7}\ \text{T}. The 3.0 \times 10^{-6}\ \text{T} value is ten times too large, a common decimal slip. The huge 2.7 \times 10^{10}\ \text{T} option comes from mistakenly multiplying by c instead of dividing. The 30 T answer would treat the relation as E_0/3 with the wrong power of ten, which is physically absurd for radiation. The numerical smallness of B_0 reflects the factor of c separating the two fields, exactly as described in the NCERT Electromagnetic Waves chapter. As a sanity check, magnetic field amplitudes in ordinary light are always extremely small, on the order of 10^{-7}\ \text{T} or less, so the chosen answer is physically reasonable.
This easy difficulty physics question is from the chapter electromagnetic waves, covering the topic of field amplitude relation. It appeared in the 2025 exam.
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