An electronmagnetic wae propagating along x-axis then oscillating electric and magnetic field vectors are along

Options

A. `E_(y)&B_(z)`
B. `E_(x)& B_(y)`
C. `E_(x)&B_(x)`
D. `E_(z)&B_(x)`

Answer

To solve the problem of determining the directions of the oscillating electric and magnetic field vectors in an electromagnetic wave propagating along the x-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Propagation Direction**:
The problem states that the electromagnetic wave is propagating along the x-axis. This means the wave travels in the positive x-direction.

2. **Identify the Relationship Between E, B, and Propagation Direction**:
In an electromagnetic wave, the electric field vector (E), the magnetic field vector (B), and the direction of wave propagation (velocity vector, v) are mutually perpendicular to each other. This is a fundamental property of electromagnetic waves.

3. **Set Up the Coordinate System**:
We can visualize the situation in a three-dimensional Cartesian coordinate system:
- Let the x-axis represent the direction of wave propagation.
- The electric field vector (E) can be oriented along either the y-axis or the z-axis.
- The magnetic field vector (B) will then be oriented along the remaining axis.

4. **Determine the Directions of E and B**:
- If we assume the electric field (E) is along the y-axis, then we can denote it as \( \vec{E} = E_y \hat{j} \).
- Since E and B must be perpendicular to each other and to the direction of propagation (x-axis), the magnetic field (B) must be along the z-axis, denoted as \( \vec{B} = B_z \hat{k} \).

5. **Confirm the Right-Hand Rule**:
To verify the orientation, we can use the right-hand rule:
- Point your thumb in the direction of the wave propagation (x-axis).
- Your index finger should point in the direction of the electric field (y-axis).
- Your middle finger, perpendicular to both, will then point in the direction of the magnetic field (z-axis).

6. **Conclusion**:
Based on the above analysis, we conclude that:
- The electric field vector (E) is along the y-axis.
- The magnetic field vector (B) is along the z-axis.

Thus, the final answer is that the electric field is along the y-axis and the magnetic field is along the z-axis.

### Answer:
- Electric Field (E) direction: y-axis
- Magnetic Field (B) direction: z-axis