Electromagnetic waves propagate in the direction parallel to the vector

Options

A. `vecE`
B. `vecB`
C. `vecExxvecB`
D. `vecBxxvecE`

Answer

To solve the question regarding the propagation direction of electromagnetic waves, we can follow these steps:

### Step 1: Understand the Components of Electromagnetic Waves
Electromagnetic waves consist of two components: the electric field vector (E) and the magnetic field vector (B). These two vectors are perpendicular to each other and also to the direction of wave propagation.

**Hint:** Remember that in electromagnetic waves, the electric and magnetic fields are always perpendicular to each other.

### Step 2: Identify the Direction of Propagation
The direction of propagation of electromagnetic waves is given by the cross product of the electric field vector (E) and the magnetic field vector (B). This means that the wave propagates in a direction that is perpendicular to both E and B.

**Hint:** The cross product of two vectors gives a third vector that is perpendicular to the plane formed by the first two vectors.

### Step 3: Use the Right-Hand Rule
To determine the direction of propagation, we can use the right-hand rule. If you point your right hand's fingers in the direction of the electric field (E) and curl them towards the direction of the magnetic field (B), your thumb will point in the direction of wave propagation.

**Hint:** The right-hand rule is a useful tool for visualizing the relationship between the vectors.

### Step 4: Write the Expression for Propagation Direction
The propagation direction of electromagnetic waves can be mathematically expressed as:
\[ \text{Propagation direction} = \mathbf{E} \times \mathbf{B} \]

This indicates that the direction of propagation is given by the cross product of the electric field vector and the magnetic field vector.

**Hint:** Remember that the order of the cross product matters; \( \mathbf{E} \times \mathbf{B} \) is not the same as \( \mathbf{B} \times \mathbf{E} \).

### Step 5: Conclusion
Based on the above analysis, we conclude that electromagnetic waves propagate in the direction given by the vector \( \mathbf{E} \times \mathbf{B} \).

**Final Answer:** The propagation direction of electromagnetic waves is parallel to the vector \( \mathbf{E} \times \mathbf{B} \).