The electric field of an electromagnetic wave in free space is represented as E⃗=E₀ cos (ω t-kz) î. The corresponding magnetic induction vector will be :

Solution

Physics sir · 4 steps

B rides along with E: same phase, same direction of travel, and its size is E divided by c.

1. Direction of travel. The phase (ω t - kz) stays constant when z grows with t, so the wave moves along +k̂. A phase (ω t + kz) would describe a wave moving along -k̂.
2. Same phase. In an EM wave, E⃗ and B⃗ oscillate together and travel together. So B⃗ must carry the same factor cos(ω t - kz).
3. Direction and size. E⃗ × B⃗ points along the direction of travel. With î × ĵ = k̂, B⃗ lies along ĵ. Its amplitude follows from the relation below.

   B₀ = E₀/c

4. So. B⃗ = E₀/c cos(ω t - kz) ĵ, which is option (b).

The idea to keep. In an EM wave, B has the same phase as E, its amplitude is E₀/c, and its direction makes E⃗ × B⃗ point along the direction of travel.

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