If the magnetic field of a light wave oscillates parallel to a y axis and is given by${\mathit{B}}_{\mathbf{y}}\mathbf{=}{\mathit{B}}_{\mathbf{m}}\mathit{s}\mathit{i}\mathit{n}\left(kz-\omega t\right)$, (a) in what direction does the wave travel and (b) parallel to which axis does the associated electric field oscillate?

The equation of the magnetic field oscillating parallel to the y axis is given as:

$B_y=B_m\sin \left(kz-\omega t\right)$

An electromagnetic wave consists of an electric field and a magnetic field, and the direction of the propagating electromagnetic wave is perpendicular to the plane in which the electric field and magnetic field lie. Thus, by analyzing the given equation, we can find the direction of the electromagnetic wave and the direction of the electric field component.

From the given equation, the term "kz" denotes that the wave travels along the z –direction.

Hence, the direction of the wave is towards the z-axis.

As the magnetic field is oscillating parallel to the y axis and the wave is traveling along the z direction. Thus, we can say that the electric field must oscillate parallel to the x-axis, perpendicular to both the directions of the propagation of the wave and the magnetic field.

Hence, the direction of the component of the electric field is towards the x-axis.