Question

Which one of the following is the property of a monochromatic, plane electromagnetic wave in free space?

• A. Electric and magnetic fields have a phase difference of \( \pi/2 \)
• B. The energy contribution of both electric and magnetic fields are equal
• C. The direction of propagation is in the direction of electric field E
• D. The pressure exerted by the wave is the product of energy density and the speed of the wave
• E. The speed of the wave is B/E

Hint:

To remember the speed relation, think of the alphabet: E comes before B, so \( E \) is in the numerator: \( c = E/B \)

Answer 1

The Correct Option is B

Concept: Electromagnetic (EM) waves have several fundamental properties as defined by Maxwell's equations and wave theory.
• Phase Relation: Electric (\( \vec{E} \)) and magnetic (\( \vec{B} \)) field vectors are in phase (\( \phi = 0 \))
• Transverse Nature: Both fields are perpendicular to each other and to the direction of propagation (\( \vec{E} \times \vec{B} \))
• Speed Relation: The speed of light in vacuum is \( c = E/B \)
• Energy Density: Energy is shared equally between the electric and magnetic components

Step 1: Evaluate the given options.

• (A) Incorrect; the fields are in phase
• (C) Incorrect; the wave propagates perpendicular to the electric field
• (D) Incorrect; radiation pressure is related to the energy density but not as a simple product with speed
• (E) Incorrect; the speed is \( E/B \), not \( B/E \)

Step 2: Identify the correct property.
As demonstrated in Question 36, for EM waves in free space, the average electric energy density (\( u_E \)) is equal to the average magnetic energy density (\( u_B \)) This makes Statement (B) the correct property