In an electromagnetic wave the electric field vector and magnetic field vector are given as E⃗ = E₀î and B⃗ = B₀k̂ respectively. The direction of propagation of electromagnetic wave is along :

Solution

Physics sir · 3 steps

The wave travels along E cross B, so work out î × k̂ carefully and watch the sign.

1. Direction rule. In an electromagnetic wave, E⃗, B⃗ and the direction of travel are mutually perpendicular. The wave moves along E⃗ × B⃗, in that order.

   E⃗ × B⃗ = E₀ B₀ (î × k̂) = E₀ B₀ (-ĵ)

2. Cyclic order. Going around î → ĵ → k̂ → î in order gives a plus sign: k̂ × î = ĵ. Going against that order flips the sign, so î × k̂ = -ĵ.
3. So. The wave propagates along -ĵ, which is option (d).

The idea to keep. Propagation is always along E⃗ × B⃗, perpendicular to both fields. Keep E first and B second, then use the cyclic order i, j, k to get the sign.

Answer from the NTA final answer key. Solution by PrepWiser.