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In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of 2.0×10¹⁰ Hz and amplitude 48 V m⁻¹. Then the amplitude of oscillating magnetic field is: (Speed of light in free space = 3×10⁸ m s⁻¹)
B₀ = E₀ / c = 48 / (3 × 10⁸) = 16 × 10⁻⁸ = 1.6 × 10⁻⁷ T in 10 seconds! (Frequency is extraneous distraction info).
According to Maxwell’s equations for a plane transverse electromagnetic wave propagating in vacuum, the magnitudes of the mutually perpendicular oscillating electric (E⃗) and magnetic (B⃗) fields are in phase and related at every instant by the speed of light c:
Rearranging the equation to solve for the peak magnetic field amplitude B₀:
Substitute the given electric field amplitude E₀ = 48 V m⁻¹ and the speed of light c = 3 × 10⁸ m s⁻¹:
Convert to canonical scientific notation:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Incorrect exponent (off by factor of 10).
Off by a factor of 100.
Wrote 1.6 × 10⁻⁸ instead of 16 × 10⁻⁸.
Accurate value: 48 / (3 × 10⁸) = 1.6 × 10⁻⁷ T.
A very common exam hall slip is writing 48/3 = 16, then seeing 10⁻⁸ in the denominator, and hastily picking Option (3) 1.6 × 10⁻⁸ without realizing 16 × 10⁻⁸ = 1.6 × 10⁻⁷.
"In vacuum, the amplitudes of electric and magnetic fields satisfy E₀ = c B₀."
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