A plane electromagnetic wave travels in free space along the `x-`direction. The electric field component of the wave at a particular point of space and time is `E=6Vm^(-1)` along `y-`direction. Its corresponding magnetic field component, `B` would be:

Options

A. `2xx10^(-8)T` along `2-`direction
B. `6xx10^(-8)T` along `x-`direction
C. `6xx10^(-8)T` along `z-`direction
D. `2xx10^(-8)T` along `y-`direction

Answer

To find the corresponding magnetic field component \( B \) of a plane electromagnetic wave traveling in free space, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Direction of Propagation and Electric Field**:
- The wave is traveling in the \( x \)-direction.
- The electric field \( E \) is given as \( 6 \, \text{V/m} \) along the \( y \)-direction.

2. **Determine the Direction of the Magnetic Field**:
- In an electromagnetic wave, the electric field \( E \), magnetic field \( B \), and the direction of wave propagation are all mutually perpendicular.
- Since the wave is traveling in the \( x \)-direction and the electric field is in the \( y \)-direction, the magnetic field \( B \) must be in the \( z \)-direction.

3. **Use the Relationship Between Electric and Magnetic Fields**:
- The relationship between the amplitudes of the electric field \( E_0 \) and magnetic field \( B_0 \) in free space is given by:
\[ \frac{E_0}{B_0} = c \]
where \( c \) is the speed of light in vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).

4. **Substitute the Known Values**:
- Given \( E_0 = 6 \, \text{V/m} \) and \( c = 3 \times 10^8 \, \text{m/s} \), we can rearrange the equation to find \( B_0 \):
\[ B_0 = \frac{E_0}{c} = \frac{6 \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} \]

5. **Calculate \( B_0 \)**:
- Performing the calculation:
\[ B_0 = \frac{6}{3 \times 10^8} = 2 \times 10^{-8} \, \text{T} \]

6. **Final Answer**:
- Therefore, the corresponding magnetic field component \( B \) is:
\[ B = 2 \times 10^{-8} \, \text{T} \, \text{along the } z\text{-direction} \]

### Summary of the Solution:
The magnetic field component corresponding to the electric field \( E = 6 \, \text{V/m} \) along the \( y \)-direction, for a wave traveling in the \( x \)-direction, is \( B = 2 \times 10^{-8} \, \text{T} \) along the \( z \)-direction.