The electric field E associated with a progressive electromagnetic wave is given by E =E₀sin(kx- ωt). If B0 is the amplitude of the magnetic field associated with the wave, then

The correct option is E₀ / B₀ = ω / k.

To understand why this relation holds, we can analyze the fundamental properties of a progressive electromagnetic wave propagating through space.

First, let's identify the given variables and parameters from the description of the wave:
The electric field component of the electromagnetic wave is given as:
$$E=E_0\sin (kx-\omega t)$$
Here, $E_0$ is the amplitude of the electric field, $k$ is the wave number (propagation constant), and $\omega$ is the angular frequency.

For any electromagnetic wave traveling in a vacuum or free space, the ratio of the amplitude of the electric field ($E_0$) to the amplitude of the magnetic field ($B_0$) is always equal to the speed of light ($c$) in that medium. This standard relation is written as:
$$\frac{E_0}{B_0}=c$$

Furthermore, the wave speed ($c$) of a progressive harmonic wave can be expressed in terms of its angular frequency ($\omega$) and wave number ($k$) by the standard wave relation:
$$c=\frac{\omega }{k}$$

By equating the two expressions for the speed of light ($c$), we obtain:
$$\frac{E_0}{B_0}=\frac{\omega }{k}$$
This matches the relation given in the correct option.