Animated Solution for Physics - Electromagnetic Waves: A plane electromagnetic wave propagating along $y$-direction can have the following pair of electric field ($\mathbf{E}$) and magnetic field ($\mathbf{B}$) components.

Imagine you are standing in a completely empty void, and suddenly, a beam of light pierces through the darkness. What exactly is that light made of?

James Clerk Maxwell beautifully demonstrated that light is an electromagnetic wave. It is a synchronized dance of electric and magnetic fields, oscillating through space and time.

But these fields don't just flail around randomly. They follow a very strict set of geometric rules. The most fundamental rule is that an electromagnetic wave is transverse in nature.

This means that the electric field vector $\mathbf{E}$, the magnetic field vector $\mathbf{B}$, and the velocity vector $\mathbf{v}$ (the direction the wave is traveling) are all mutually perpendicular to each other.

In our specific problem, we are told that the plane electromagnetic wave is propagating along the $y$-direction.

Let's visualize our 3D coordinate system. We have the $x$-axis, the $y$-axis, and the $z$-axis. The wave is marching steadily along the $y$-axis.

Because of the transverse nature of the wave, the electric and magnetic fields must oscillate in a plane that is completely perpendicular to the $y$-axis.

What plane is perpendicular to the $y$-axis? It is the $xz$-plane.

This geometric constraint is incredibly powerful. If the fields are entirely confined to the $xz$-plane, they cannot have any component pointing in the $y$-direction.

Mathematically, this means that the $y$-component of the electric field, $E_y$, must be exactly zero. Similarly, the $y$-component of the magnetic field, $B_y$, must also be exactly zero.

Let's look at the options provided in the question. Any option that suggests the presence of $E_y$ or $B_y$ is physically impossible for a wave traveling along the $y$-axis.

Option (a) suggests $E_y,B_y$. This is incorrect. Option (b) suggests $E_y,B_x$. This is incorrect. Option (d) suggests $E_x,B_y$. This is also incorrect.

By simple elimination, we are left with only one physically viable option.

The fields must be composed of $x$ and $z$ components. If the electric field is oscillating along the $x$-axis ($E_x$), then the magnetic field must oscillate along the $z$-axis ($B_z$) to remain perpendicular to both the electric field and the direction of propagation.

Conversely, if the electric field is along the $z$-axis ($E_z$), the magnetic field must be along the $x$-axis ($B_x$).

Therefore, the possible pairs of components are $E_x,B_z$ or $E_z,B_x$.

This perfectly matches option (c). The elegance of this problem lies in how a deep physical principle—the transverse nature of light—allows us to solve it without writing down a single complex equation!