Electromagnetic Waves · Vector Phase

Extract direction, wave number and frequency from the phase

The electric field is E₀ sin(3y + 4z + ωt) î. The spatial part fixes the wave vector magnitude, while the plus sign before ωt tells us the wave travels opposite to 3ĵ + 4k̂.

2026 Paper 1 Q8 · EM wave in the yz-plane
Statement check
Read the phase
The phase is 3y + 4z + ωt, so the wave vector is 3ĵ + 4k̂ but propagation is opposite to it.
Relation|k| = √(3² + 4²) = 5 m⁻¹
VerdictA and C are correct
Electric fieldalong î
Propagationopposite to 3ĵ + 4k̂
Magnetic fieldperpendicular to E and direction

Derivation path

01 / DIRECTION

The sign before ωt matters

A phase of k·r + ωt represents travel in the −k direction.

direction = −(3ĵ + 4k̂)/5
02 / WAVE NUMBER

Magnitude is not 0.5

The spatial coefficients are 3 and 4, so the wave-vector magnitude is 5 m⁻¹.

|k| = √(3² + 4²) = 5 m⁻¹
03 / VACUUM RELATION

Use ω = ck

In vacuum, the angular frequency is the speed of light multiplied by the wave number.

ω = 3 × 10⁸ × 5 = 1.5 × 10⁹ rad s⁻¹
Correct statements
Statement A is true because the wave travels in −(3ĵ + 4k̂)/5.
Statement C is true because |k| = 5 m⁻¹ and ω = c|k| = 1.5 × 10⁹ rad s⁻¹.
Correct answer: A and C