The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
Eₓ = Eₒ sin (kz - ω t)
B_y = Bₒ sin (kz - ω t)
Then the correct relation between E₀ and B₀ is given by

Solution

Physics sir · 4 steps

In vacuum, E₀/B₀ is the wave speed c, and the wave speed is ω/k. Put those two together.

1. Field ratio. For any EM wave in vacuum, the amplitudes of the electric and magnetic fields are linked by the speed of light: E₀ = cB₀.
2. Speed from phase. The phase kz - ω t stays constant when z grows at the rate dz/dt = ω/k. That rate is the wave speed, so c = ω/k.

   E₀/B₀ = c = ω/k ⇒ kE₀ = ω B₀

3. Quick check. Faraday's law gives the same result. Here it reads (∂ Eₓ)/(∂ z) = -(∂ B_y)/(∂ t), which gives kE₀cos(kz - ω t) = ω B₀cos(kz - ω t).
4. So. The correct relation is kE₀ = ω B₀, which is option (c).

The idea to keep. Two facts carry every question of this kind: E₀ = cB₀, and the speed read off the phase is c = ω/k. Check the units of your final relation before you choose an option.

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