Question: In an electromagnetic wave, the electric field ($\vec{E}$) and the magnetic field ($\vec{B}$) oscillate along x-axis and y-axis respectively. The wave is propagating along :

Step 1 (Governing Law): [0.5 Mark]

The direction of propagation of an electromagnetic wave is given by the direction of the Poynting vector ($\vec{S}$), which is defined by the cross product of the electric field vector ($\vec{E}$) and the magnetic field vector ($\vec{B}$):

Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]

• Given: $\vec{E}$ is along the x-axis, so $\vec{E} = E_0 \hat{i}$
• Given: $\vec{B}$ is along the y-axis, so $\vec{B} = B_0 \hat{j}$
• The direction of propagation is determined by the unit vector:
$$\hat{n} = \hat{i} \times \hat{j}$$
• Using the properties of orthogonal unit vectors:
$$\hat{i} \times \hat{j} = \hat{k}$$

Step 3 (Final Concluded Answer): [0.25 Mark]

Since the result of the cross product is $\hat{k}$, the electromagnetic wave propagates along the z-axis.

Correct Option: (A) z-axis

💡 EL10 Concept Insight: Think of the electric and magnetic fields as two people holding a rope; if one shakes it up-down and the other side-to-side, the wave energy naturally travels forward in the only direction left open, which is straight ahead (the z-axis).